text: from math import ceil
  
  from django.utils import six
  
  
  class InvalidPage(Exception):
      pass
  
  class PageNotAnInteger(InvalidPage):
      pass
  
  class EmptyPage(InvalidPage):
      pass
  
  class Paginator(object):
      def __init__(self, object_list, per_page, orphans=0, allow_empty_first_page=True):
          self.object_list = object_list
          self.per_page = int(per_page)
          self.orphans = int(orphans)
          self.allow_empty_first_page = allow_empty_first_page
          self._num_pages = self._count = None
  
      def validate_number(self, number):
          "Validates the given 1-based page number."
          try:
              number = int(number)
          except (TypeError, ValueError):
              raise PageNotAnInteger('That page number is not an integer')
          if number < 1:
              raise EmptyPage('That page number is less than 1')
          if number > self.num_pages:
              if number == 1 and self.allow_empty_first_page:
                  pass
              else:
                  raise EmptyPage('That page contains no results')
          return number
  
      def page(self, number):
          "Returns a Page object for the given 1-based page number."
          number = self.validate_number(number)
          bottom = (number - 1) * self.per_page
          top = bottom + self.per_page
          if top + self.orphans >= self.count:
              top = self.count
          return Page(self.object_list[bottom:top], number, self)
  
      def _get_count(self):
          "Returns the total number of objects, across all pages."
          if self._count is None:
              try:
                  self._count = self.object_list.count()
              except (AttributeError, TypeError):
                  # AttributeError if object_list has no count() method.
                  # TypeError if object_list.count() requires arguments
                  # (i.e. is of type list).
                  self._count = len(self.object_list)
          return self._count
      count = property(_get_count)
  
      def _get_num_pages(self):
          "Returns the total number of pages."
          if self._num_pages is None:
              if self.count == 0 and not self.allow_empty_first_page:
                  self._num_pages = 0
              else:
                  hits = max(1, self.count - self.orphans)
                  self._num_pages = int(ceil(hits / float(self.per_page)))
          return self._num_pages
      num_pages = property(_get_num_pages)
  
      def _get_page_range(self):
          """
          Returns a 1-based range of pages for iterating through within
          a template for loop.
          """
          return range(1, self.num_pages + 1)
      page_range = property(_get_page_range)
  
  QuerySetPaginator = Paginator # For backwards-compatibility.
  
  class Page(object):
      def __init__(self, object_list, number, paginator):
          self.object_list = object_list
          self.number = number
          self.paginator = paginator
  
      def __repr__(self):
          return '<Page %s of %s>' % (self.number, self.paginator.num_pages)
  
      def __len__(self):
          return len(self.object_list)
  
      def __getitem__(self, index):
          if not isinstance(index, (slice,) + six.integer_types):
              raise TypeError
          # The object_list is converted to a list so that if it was a QuerySet
          # it won't be a database hit per __getitem__.
          return list(self.object_list)[index]
  
      # The following four methods are only necessary for Python <2.6
      # compatibility (this class could just extend 2.6's collections.Sequence).
  
      def __iter__(self):
          i = 0
          try:
              while True:
                  v = self[i]
                  yield v
                  i += 1
          except IndexError:
              return
  
      def __contains__(self, value):
          for v in self:
              if v == value:
                  return True
          return False
  
      def index(self, value):
          for i, v in enumerate(self):
              if v == value:
                  return i
          raise ValueError
  
      def count(self, value):
          return sum([1 for v in self if v == value])
  
      # End of compatibility methods.
  
      def has_next(self):
          return self.number < self.paginator.num_pages
  
      def has_previous(self):
          return self.number > 1
  
      def has_other_pages(self):
          return self.has_previous() or self.has_next()
  
      def next_page_number(self):
          return self.paginator.validate_number(self.number + 1)
  
      def previous_page_number(self):
          return self.paginator.validate_number(self.number - 1)
  
      def start_index(self):
          """
          Returns the 1-based index of the first object on this page,
          relative to total objects in the paginator.
          """
          # Special case, return zero if no items.
          if self.paginator.count == 0:
              return 0
          return (self.paginator.per_page * (self.number - 1)) + 1
  
      def end_index(self):
          """
          Returns the 1-based index of the last object on this page,
          relative to total objects found (hits).
          """
          # Special case for the last page because there can be orphans.
          if self.number == self.paginator.num_pages:
              return self.paginator.count
          return self.number * self.paginator.per_page
  