text: import functools
  import inspect
  from functools import partial
  
  from django import forms
  from django.apps import apps
  from django.core import checks, exceptions
  from django.db import connection, router
  from django.db.backends import utils
  from django.db.models import Q
  from django.db.models.constants import LOOKUP_SEP
  from django.db.models.deletion import CASCADE, SET_DEFAULT, SET_NULL
  from django.db.models.query_utils import PathInfo
  from django.db.models.utils import make_model_tuple
  from django.utils.functional import cached_property
  from django.utils.translation import gettext_lazy as _
  
  from . import Field
  from .mixins import FieldCacheMixin
  from .related_descriptors import (
      ForwardManyToOneDescriptor, ForwardOneToOneDescriptor,
      ManyToManyDescriptor, ReverseManyToOneDescriptor,
      ReverseOneToOneDescriptor,
  )
  from .related_lookups import (
      RelatedExact, RelatedGreaterThan, RelatedGreaterThanOrEqual, RelatedIn,
      RelatedIsNull, RelatedLessThan, RelatedLessThanOrEqual,
  )
  from .reverse_related import (
      ForeignObjectRel, ManyToManyRel, ManyToOneRel, OneToOneRel,
  )
  
  RECURSIVE_RELATIONSHIP_CONSTANT = 'self'
  
  
  def resolve_relation(scope_model, relation):
      """
      Transform relation into a model or fully-qualified model string of the form
      "app_label.ModelName", relative to scope_model.
  
      The relation argument can be:
        * RECURSIVE_RELATIONSHIP_CONSTANT, i.e. the string "self", in which case
          the model argument will be returned.
        * A bare model name without an app_label, in which case scope_model's
          app_label will be prepended.
        * An "app_label.ModelName" string.
        * A model class, which will be returned unchanged.
      """
      # Check for recursive relations
      if relation == RECURSIVE_RELATIONSHIP_CONSTANT:
          relation = scope_model
  
      # Look for an "app.Model" relation
      if isinstance(relation, str):
          if "." not in relation:
              relation = "%s.%s" % (scope_model._meta.app_label, relation)
  
      return relation
  
  
  def lazy_related_operation(function, model, *related_models, **kwargs):
      """
      Schedule `function` to be called once `model` and all `related_models`
      have been imported and registered with the app registry. `function` will
      be called with the newly-loaded model classes as its positional arguments,
      plus any optional keyword arguments.
  
      The `model` argument must be a model class. Each subsequent positional
      argument is another model, or a reference to another model - see
      `resolve_relation()` for the various forms these may take. Any relative
      references will be resolved relative to `model`.
  
      This is a convenience wrapper for `Apps.lazy_model_operation` - the app
      registry model used is the one found in `model._meta.apps`.
      """
      models = [model] + [resolve_relation(model, rel) for rel in related_models]
      model_keys = (make_model_tuple(m) for m in models)
      apps = model._meta.apps
      return apps.lazy_model_operation(partial(function, **kwargs), *model_keys)
  
  
  class RelatedField(FieldCacheMixin, Field):
      """Base class that all relational fields inherit from."""
  
      # Field flags
      one_to_many = False
      one_to_one = False
      many_to_many = False
      many_to_one = False
  
      @cached_property
      def related_model(self):
          # Can't cache this property until all the models are loaded.
          apps.check_models_ready()
          return self.remote_field.model
  
      def check(self, **kwargs):
          return [
              *super().check(**kwargs),
              *self._check_related_name_is_valid(),
              *self._check_related_query_name_is_valid(),
              *self._check_relation_model_exists(),
              *self._check_referencing_to_swapped_model(),
              *self._check_clashes(),
          ]
  
      def _check_related_name_is_valid(self):
          import keyword
          related_name = self.remote_field.related_name
          if related_name is None:
              return []
          is_valid_id = not keyword.iskeyword(related_name) and related_name.isidentifier()
          if not (is_valid_id or related_name.endswith('+')):
              return [
                  checks.Error(
                      "The name '%s' is invalid related_name for field %s.%s" %
                      (self.remote_field.related_name, self.model._meta.object_name,
                       self.name),
                      hint="Related name must be a valid Python identifier or end with a '+'",
                      obj=self,
                      id='fields.E306',
                  )
              ]
          return []
  
      def _check_related_query_name_is_valid(self):
          if self.remote_field.is_hidden():
              return []
          rel_query_name = self.related_query_name()
          errors = []
          if rel_query_name.endswith('_'):
              errors.append(
                  checks.Error(
                      "Reverse query name '%s' must not end with an underscore."
                      % (rel_query_name,),
                      hint=("Add or change a related_name or related_query_name "
                            "argument for this field."),
                      obj=self,
                      id='fields.E308',
                  )
              )
          if LOOKUP_SEP in rel_query_name:
              errors.append(
                  checks.Error(
                      "Reverse query name '%s' must not contain '%s'."
                      % (rel_query_name, LOOKUP_SEP),
                      hint=("Add or change a related_name or related_query_name "
                            "argument for this field."),
                      obj=self,
                      id='fields.E309',
                  )
              )
          return errors
  
      def _check_relation_model_exists(self):
          rel_is_missing = self.remote_field.model not in self.opts.apps.get_models()
          rel_is_string = isinstance(self.remote_field.model, str)
          model_name = self.remote_field.model if rel_is_string else self.remote_field.model._meta.object_name
          if rel_is_missing and (rel_is_string or not self.remote_field.model._meta.swapped):
              return [
                  checks.Error(
                      "Field defines a relation with model '%s', which is either "
                      "not installed, or is abstract." % model_name,
                      obj=self,
                      id='fields.E300',
                  )
              ]
          return []
  
      def _check_referencing_to_swapped_model(self):
          if (self.remote_field.model not in self.opts.apps.get_models() and
                  not isinstance(self.remote_field.model, str) and
                  self.remote_field.model._meta.swapped):
              model = "%s.%s" % (
                  self.remote_field.model._meta.app_label,
                  self.remote_field.model._meta.object_name
              )
              return [
                  checks.Error(
                      "Field defines a relation with the model '%s', which has "
                      "been swapped out." % model,
                      hint="Update the relation to point at 'settings.%s'." % self.remote_field.model._meta.swappable,
                      obj=self,
                      id='fields.E301',
                  )
              ]
          return []
  
      def _check_clashes(self):
          """Check accessor and reverse query name clashes."""
          from django.db.models.base import ModelBase
  
          errors = []
          opts = self.model._meta
  
          # `f.remote_field.model` may be a string instead of a model. Skip if model name is
          # not resolved.
          if not isinstance(self.remote_field.model, ModelBase):
              return []
  
          # Consider that we are checking field `Model.foreign` and the models
          # are:
          #
          #     class Target(models.Model):
          #         model = models.IntegerField()
          #         model_set = models.IntegerField()
          #
          #     class Model(models.Model):
          #         foreign = models.ForeignKey(Target)
          #         m2m = models.ManyToManyField(Target)
  
          # rel_opts.object_name == "Target"
          rel_opts = self.remote_field.model._meta
          # If the field doesn't install a backward relation on the target model
          # (so `is_hidden` returns True), then there are no clashes to check
          # and we can skip these fields.
          rel_is_hidden = self.remote_field.is_hidden()
          rel_name = self.remote_field.get_accessor_name()  # i. e. "model_set"
          rel_query_name = self.related_query_name()  # i. e. "model"
          field_name = "%s.%s" % (opts.object_name, self.name)  # i. e. "Model.field"
  
          # Check clashes between accessor or reverse query name of `field`
          # and any other field name -- i.e. accessor for Model.foreign is
          # model_set and it clashes with Target.model_set.
          potential_clashes = rel_opts.fields + rel_opts.many_to_many
          for clash_field in potential_clashes:
              clash_name = "%s.%s" % (rel_opts.object_name, clash_field.name)  # i.e. "Target.model_set"
              if not rel_is_hidden and clash_field.name == rel_name:
                  errors.append(
                      checks.Error(
                          "Reverse accessor for '%s' clashes with field name '%s'." % (field_name, clash_name),
                          hint=("Rename field '%s', or add/change a related_name "
                                "argument to the definition for field '%s'.") % (clash_name, field_name),
                          obj=self,
                          id='fields.E302',
                      )
                  )
  
              if clash_field.name == rel_query_name:
                  errors.append(
                      checks.Error(
                          "Reverse query name for '%s' clashes with field name '%s'." % (field_name, clash_name),
                          hint=("Rename field '%s', or add/change a related_name "
                                "argument to the definition for field '%s'.") % (clash_name, field_name),
                          obj=self,
                          id='fields.E303',
                      )
                  )
  
          # Check clashes between accessors/reverse query names of `field` and
          # any other field accessor -- i. e. Model.foreign accessor clashes with
          # Model.m2m accessor.
          potential_clashes = (r for r in rel_opts.related_objects if r.field is not self)
          for clash_field in potential_clashes:
              clash_name = "%s.%s" % (  # i. e. "Model.m2m"
                  clash_field.related_model._meta.object_name,
                  clash_field.field.name)
              if not rel_is_hidden and clash_field.get_accessor_name() == rel_name:
                  errors.append(
                      checks.Error(
                          "Reverse accessor for '%s' clashes with reverse accessor for '%s'." % (field_name, clash_name),
                          hint=("Add or change a related_name argument "
                                "to the definition for '%s' or '%s'.") % (field_name, clash_name),
                          obj=self,
                          id='fields.E304',
                      )
                  )
  
              if clash_field.get_accessor_name() == rel_query_name:
                  errors.append(
                      checks.Error(
                          "Reverse query name for '%s' clashes with reverse query name for '%s'."
                          % (field_name, clash_name),
                          hint=("Add or change a related_name argument "
                                "to the definition for '%s' or '%s'.") % (field_name, clash_name),
                          obj=self,
                          id='fields.E305',
                      )
                  )
  
          return errors
  
      def db_type(self, connection):
          # By default related field will not have a column as it relates to
          # columns from another table.
          return None
  
      def contribute_to_class(self, cls, name, private_only=False, **kwargs):
  
          super().contribute_to_class(cls, name, private_only=private_only, **kwargs)
  
          self.opts = cls._meta
  
          if not cls._meta.abstract:
              if self.remote_field.related_name:
                  related_name = self.remote_field.related_name
              else:
                  related_name = self.opts.default_related_name
              if related_name:
                  related_name = related_name % {
                      'class': cls.__name__.lower(),
                      'model_name': cls._meta.model_name.lower(),
                      'app_label': cls._meta.app_label.lower()
                  }
                  self.remote_field.related_name = related_name
  
              if self.remote_field.related_query_name:
                  related_query_name = self.remote_field.related_query_name % {
                      'class': cls.__name__.lower(),
                      'app_label': cls._meta.app_label.lower(),
                  }
                  self.remote_field.related_query_name = related_query_name
  
              def resolve_related_class(model, related, field):
                  field.remote_field.model = related
                  field.do_related_class(related, model)
              lazy_related_operation(resolve_related_class, cls, self.remote_field.model, field=self)
  
      def deconstruct(self):
          name, path, args, kwargs = super().deconstruct()
          if self.remote_field.limit_choices_to:
              kwargs['limit_choices_to'] = self.remote_field.limit_choices_to
          if self.remote_field.related_name is not None:
              kwargs['related_name'] = self.remote_field.related_name
          if self.remote_field.related_query_name is not None:
              kwargs['related_query_name'] = self.remote_field.related_query_name
          return name, path, args, kwargs
  
      def get_forward_related_filter(self, obj):
          """
          Return the keyword arguments that when supplied to
          self.model.object.filter(), would select all instances related through
          this field to the remote obj. This is used to build the querysets
          returned by related descriptors. obj is an instance of
          self.related_field.model.
          """
          return {
              '%s__%s' % (self.name, rh_field.name): getattr(obj, rh_field.attname)
              for _, rh_field in self.related_fields
          }
  
      def get_reverse_related_filter(self, obj):
          """
          Complement to get_forward_related_filter(). Return the keyword
          arguments that when passed to self.related_field.model.object.filter()
          select all instances of self.related_field.model related through
          this field to obj. obj is an instance of self.model.
          """
          base_filter = {
              rh_field.attname: getattr(obj, lh_field.attname)
              for lh_field, rh_field in self.related_fields
          }
          descriptor_filter = self.get_extra_descriptor_filter(obj)
          base_q = Q(**base_filter)
          if isinstance(descriptor_filter, dict):
              return base_q & Q(**descriptor_filter)
          elif descriptor_filter:
              return base_q & descriptor_filter
          return base_q
  
      @property
      def swappable_setting(self):
          """
          Get the setting that this is powered from for swapping, or None
          if it's not swapped in / marked with swappable=False.
          """
          if self.swappable:
              # Work out string form of "to"
              if isinstance(self.remote_field.model, str):
                  to_string = self.remote_field.model
              else:
                  to_string = self.remote_field.model._meta.label
              return apps.get_swappable_settings_name(to_string)
          return None
  
      def set_attributes_from_rel(self):
          self.name = (
              self.name or
              (self.remote_field.model._meta.model_name + '_' + self.remote_field.model._meta.pk.name)
          )
          if self.verbose_name is None:
              self.verbose_name = self.remote_field.model._meta.verbose_name
          self.remote_field.set_field_name()
  
      def do_related_class(self, other, cls):
          self.set_attributes_from_rel()
          self.contribute_to_related_class(other, self.remote_field)
  
      def get_limit_choices_to(self):
          """
          Return ``limit_choices_to`` for this model field.
  
          If it is a callable, it will be invoked and the result will be
          returned.
          """
          if callable(self.remote_field.limit_choices_to):
              return self.remote_field.limit_choices_to()
          return self.remote_field.limit_choices_to
  
      def formfield(self, **kwargs):
          """
          Pass ``limit_choices_to`` to the field being constructed.
  
          Only passes it if there is a type that supports related fields.
          This is a similar strategy used to pass the ``queryset`` to the field
          being constructed.
          """
          defaults = {}
          if hasattr(self.remote_field, 'get_related_field'):
              # If this is a callable, do not invoke it here. Just pass
              # it in the defaults for when the form class will later be
              # instantiated.
              limit_choices_to = self.remote_field.limit_choices_to
              defaults.update({
                  'limit_choices_to': limit_choices_to,
              })
          defaults.update(kwargs)
          return super().formfield(**defaults)
  
      def related_query_name(self):
          """
          Define the name that can be used to identify this related object in a
          table-spanning query.
          """
          return self.remote_field.related_query_name or self.remote_field.related_name or self.opts.model_name
  
      @property
      def target_field(self):
          """
          When filtering against this relation, return the field on the remote
          model against which the filtering should happen.
          """
          target_fields = self.get_path_info()[-1].target_fields
          if len(target_fields) > 1:
              raise exceptions.FieldError(
                  "The relation has multiple target fields, but only single target field was asked for")
          return target_fields[0]
  
      def get_cache_name(self):
          return self.name
  
  
  class ForeignObject(RelatedField):
      """
      Abstraction of the ForeignKey relation to support multi-column relations.
      """
  
      # Field flags
      many_to_many = False
      many_to_one = True
      one_to_many = False
      one_to_one = False
  
      requires_unique_target = True
      related_accessor_class = ReverseManyToOneDescriptor
      forward_related_accessor_class = ForwardManyToOneDescriptor
      rel_class = ForeignObjectRel
  
      def __init__(self, to, on_delete, from_fields, to_fields, rel=None, related_name=None,
                   related_query_name=None, limit_choices_to=None, parent_link=False,
                   swappable=True, **kwargs):
  
          if rel is None:
              rel = self.rel_class(
                  self, to,
                  related_name=related_name,
                  related_query_name=related_query_name,
                  limit_choices_to=limit_choices_to,
                  parent_link=parent_link,
                  on_delete=on_delete,
              )
  
          super().__init__(rel=rel, **kwargs)
  
          self.from_fields = from_fields
          self.to_fields = to_fields
          self.swappable = swappable
  
      def check(self, **kwargs):
          return [
              *super().check(**kwargs),
              *self._check_to_fields_exist(),
              *self._check_unique_target(),
          ]
  
      def _check_to_fields_exist(self):
          # Skip nonexistent models.
          if isinstance(self.remote_field.model, str):
              return []
  
          errors = []
          for to_field in self.to_fields:
              if to_field:
                  try:
                      self.remote_field.model._meta.get_field(to_field)
                  except exceptions.FieldDoesNotExist:
                      errors.append(
                          checks.Error(
                              "The to_field '%s' doesn't exist on the related "
                              "model '%s'."
                              % (to_field, self.remote_field.model._meta.label),
                              obj=self,
                              id='fields.E312',
                          )
                      )
          return errors
  
      def _check_unique_target(self):
          rel_is_string = isinstance(self.remote_field.model, str)
          if rel_is_string or not self.requires_unique_target:
              return []
  
          try:
              self.foreign_related_fields
          except exceptions.FieldDoesNotExist:
              return []
  
          if not self.foreign_related_fields:
              return []
  
          unique_foreign_fields = {
              frozenset([f.name])
              for f in self.remote_field.model._meta.get_fields()
              if getattr(f, 'unique', False)
          }
          unique_foreign_fields.update({
              frozenset(ut)
              for ut in self.remote_field.model._meta.unique_together
          })
          foreign_fields = {f.name for f in self.foreign_related_fields}
          has_unique_constraint = any(u <= foreign_fields for u in unique_foreign_fields)
  
          if not has_unique_constraint and len(self.foreign_related_fields) > 1:
              field_combination = ', '.join(
                  "'%s'" % rel_field.name for rel_field in self.foreign_related_fields
              )
              model_name = self.remote_field.model.__name__
              return [
                  checks.Error(
                      "No subset of the fields %s on model '%s' is unique."
                      % (field_combination, model_name),
                      hint=(
                          "Add unique=True on any of those fields or add at "
                          "least a subset of them to a unique_together constraint."
                      ),
                      obj=self,
                      id='fields.E310',
                  )
              ]
          elif not has_unique_constraint:
              field_name = self.foreign_related_fields[0].name
              model_name = self.remote_field.model.__name__
              return [
                  checks.Error(
                      "'%s.%s' must set unique=True because it is referenced by "
                      "a foreign key." % (model_name, field_name),
                      obj=self,
                      id='fields.E311',
                  )
              ]
          else:
              return []
  
      def deconstruct(self):
          name, path, args, kwargs = super().deconstruct()
          kwargs['on_delete'] = self.remote_field.on_delete
          kwargs['from_fields'] = self.from_fields
          kwargs['to_fields'] = self.to_fields
  
          if self.remote_field.parent_link:
              kwargs['parent_link'] = self.remote_field.parent_link
          # Work out string form of "to"
          if isinstance(self.remote_field.model, str):
              kwargs['to'] = self.remote_field.model
          else:
              kwargs['to'] = "%s.%s" % (
                  self.remote_field.model._meta.app_label,
                  self.remote_field.model._meta.object_name,
              )
          # If swappable is True, then see if we're actually pointing to the target
          # of a swap.
          swappable_setting = self.swappable_setting
          if swappable_setting is not None:
              # If it's already a settings reference, error
              if hasattr(kwargs['to'], "setting_name"):
                  if kwargs['to'].setting_name != swappable_setting:
                      raise ValueError(
                          "Cannot deconstruct a ForeignKey pointing to a model "
                          "that is swapped in place of more than one model (%s and %s)"
                          % (kwargs['to'].setting_name, swappable_setting)
                      )
              # Set it
              from django.db.migrations.writer import SettingsReference
              kwargs['to'] = SettingsReference(
                  kwargs['to'],
                  swappable_setting,
              )
          return name, path, args, kwargs
  
      def resolve_related_fields(self):
          if not self.from_fields or len(self.from_fields) != len(self.to_fields):
              raise ValueError('Foreign Object from and to fields must be the same non-zero length')
          if isinstance(self.remote_field.model, str):
              raise ValueError('Related model %r cannot be resolved' % self.remote_field.model)
          related_fields = []
          for index in range(len(self.from_fields)):
              from_field_name = self.from_fields[index]
              to_field_name = self.to_fields[index]
              from_field = (self if from_field_name == 'self'
                            else self.opts.get_field(from_field_name))
              to_field = (self.remote_field.model._meta.pk if to_field_name is None
                          else self.remote_field.model._meta.get_field(to_field_name))
              related_fields.append((from_field, to_field))
          return related_fields
  
      @property
      def related_fields(self):
          if not hasattr(self, '_related_fields'):
              self._related_fields = self.resolve_related_fields()
          return self._related_fields
  
      @property
      def reverse_related_fields(self):
          return [(rhs_field, lhs_field) for lhs_field, rhs_field in self.related_fields]
  
      @property
      def local_related_fields(self):
          return tuple(lhs_field for lhs_field, rhs_field in self.related_fields)
  
      @property
      def foreign_related_fields(self):
          return tuple(rhs_field for lhs_field, rhs_field in self.related_fields if rhs_field)
  
      def get_local_related_value(self, instance):
          return self.get_instance_value_for_fields(instance, self.local_related_fields)
  
      def get_foreign_related_value(self, instance):
          return self.get_instance_value_for_fields(instance, self.foreign_related_fields)
  
      @staticmethod
      def get_instance_value_for_fields(instance, fields):
          ret = []
          opts = instance._meta
          for field in fields:
              # Gotcha: in some cases (like fixture loading) a model can have
              # different values in parent_ptr_id and parent's id. So, use
              # instance.pk (that is, parent_ptr_id) when asked for instance.id.
              if field.primary_key:
                  possible_parent_link = opts.get_ancestor_link(field.model)
                  if (not possible_parent_link or
                          possible_parent_link.primary_key or
                          possible_parent_link.model._meta.abstract):
                      ret.append(instance.pk)
                      continue
              ret.append(getattr(instance, field.attname))
          return tuple(ret)
  
      def get_attname_column(self):
          attname, column = super().get_attname_column()
          return attname, None
  
      def get_joining_columns(self, reverse_join=False):
          source = self.reverse_related_fields if reverse_join else self.related_fields
          return tuple((lhs_field.column, rhs_field.column) for lhs_field, rhs_field in source)
  
      def get_reverse_joining_columns(self):
          return self.get_joining_columns(reverse_join=True)
  
      def get_extra_descriptor_filter(self, instance):
          """
          Return an extra filter condition for related object fetching when
          user does 'instance.fieldname', that is the extra filter is used in
          the descriptor of the field.
  
          The filter should be either a dict usable in .filter(**kwargs) call or
          a Q-object. The condition will be ANDed together with the relation's
          joining columns.
  
          A parallel method is get_extra_restriction() which is used in
          JOIN and subquery conditions.
          """
          return {}
  
      def get_extra_restriction(self, where_class, alias, related_alias):
          """
          Return a pair condition used for joining and subquery pushdown. The
          condition is something that responds to as_sql(compiler, connection)
          method.
  
          Note that currently referring both the 'alias' and 'related_alias'
          will not work in some conditions, like subquery pushdown.
  
          A parallel method is get_extra_descriptor_filter() which is used in
          instance.fieldname related object fetching.
          """
          return None
  
      def get_path_info(self, filtered_relation=None):
          """Get path from this field to the related model."""
          opts = self.remote_field.model._meta
          from_opts = self.model._meta
          return [PathInfo(
              from_opts=from_opts,
              to_opts=opts,
              target_fields=self.foreign_related_fields,
              join_field=self,
              m2m=False,
              direct=True,
              filtered_relation=filtered_relation,
          )]
  
      def get_reverse_path_info(self, filtered_relation=None):
          """Get path from the related model to this field's model."""
          opts = self.model._meta
          from_opts = self.remote_field.model._meta
          return [PathInfo(
              from_opts=from_opts,
              to_opts=opts,
              target_fields=(opts.pk,),
              join_field=self.remote_field,
              m2m=not self.unique,
              direct=False,
              filtered_relation=filtered_relation,
          )]
  
      @classmethod
      @functools.lru_cache(maxsize=None)
      def get_lookups(cls):
          bases = inspect.getmro(cls)
          bases = bases[:bases.index(ForeignObject) + 1]
          class_lookups = [parent.__dict__.get('class_lookups', {}) for parent in bases]
          return cls.merge_dicts(class_lookups)
  
      def contribute_to_class(self, cls, name, private_only=False, **kwargs):
          super().contribute_to_class(cls, name, private_only=private_only, **kwargs)
          setattr(cls, self.name, self.forward_related_accessor_class(self))
  
      def contribute_to_related_class(self, cls, related):
          # Internal FK's - i.e., those with a related name ending with '+' -
          # and swapped models don't get a related descriptor.
          if not self.remote_field.is_hidden() and not related.related_model._meta.swapped:
              setattr(cls._meta.concrete_model, related.get_accessor_name(), self.related_accessor_class(related))
              # While 'limit_choices_to' might be a callable, simply pass
              # it along for later - this is too early because it's still
              # model load time.
              if self.remote_field.limit_choices_to:
                  cls._meta.related_fkey_lookups.append(self.remote_field.limit_choices_to)
  
  
  ForeignObject.register_lookup(RelatedIn)
  ForeignObject.register_lookup(RelatedExact)
  ForeignObject.register_lookup(RelatedLessThan)
  ForeignObject.register_lookup(RelatedGreaterThan)
  ForeignObject.register_lookup(RelatedGreaterThanOrEqual)
  ForeignObject.register_lookup(RelatedLessThanOrEqual)
  ForeignObject.register_lookup(RelatedIsNull)
  
  
  class ForeignKey(ForeignObject):
      """
      Provide a many-to-one relation by adding a column to the local model
      to hold the remote value.
  
      By default ForeignKey will target the pk of the remote model but this
      behavior can be changed by using the ``to_field`` argument.
      """
  
      # Field flags
      many_to_many = False
      many_to_one = True
      one_to_many = False
      one_to_one = False
  
      rel_class = ManyToOneRel
  
      empty_strings_allowed = False
      default_error_messages = {
          'invalid': _('%(model)s instance with %(field)s %(value)r does not exist.')
      }
      description = _("Foreign Key (type determined by related field)")
  
      def __init__(self, to, on_delete, related_name=None, related_query_name=None,
                   limit_choices_to=None, parent_link=False, to_field=None,
                   db_constraint=True, **kwargs):
          try:
              to._meta.model_name
          except AttributeError:
              assert isinstance(to, str), (
                  "%s(%r) is invalid. First parameter to ForeignKey must be "
                  "either a model, a model name, or the string %r" % (
                      self.__class__.__name__, to,
                      RECURSIVE_RELATIONSHIP_CONSTANT,
                  )
              )
          else:
              # For backwards compatibility purposes, we need to *try* and set
              # the to_field during FK construction. It won't be guaranteed to
              # be correct until contribute_to_class is called. Refs #12190.
              to_field = to_field or (to._meta.pk and to._meta.pk.name)
  
          kwargs['rel'] = self.rel_class(
              self, to, to_field,
              related_name=related_name,
              related_query_name=related_query_name,
              limit_choices_to=limit_choices_to,
              parent_link=parent_link,
              on_delete=on_delete,
          )
          kwargs.setdefault('db_index', True)
  
          super().__init__(to, on_delete, from_fields=['self'], to_fields=[to_field], **kwargs)
  
          self.db_constraint = db_constraint
  
      def check(self, **kwargs):
          return [
              *super().check(**kwargs),
              *self._check_on_delete(),
              *self._check_unique(),
          ]
  
      def _check_on_delete(self):
          on_delete = getattr(self.remote_field, 'on_delete', None)
          if on_delete == SET_NULL and not self.null:
              return [
                  checks.Error(
                      'Field specifies on_delete=SET_NULL, but cannot be null.',
                      hint='Set null=True argument on the field, or change the on_delete rule.',
                      obj=self,
                      id='fields.E320',
                  )
              ]
          elif on_delete == SET_DEFAULT and not self.has_default():
              return [
                  checks.Error(
                      'Field specifies on_delete=SET_DEFAULT, but has no default value.',
                      hint='Set a default value, or change the on_delete rule.',
                      obj=self,
                      id='fields.E321',
                  )
              ]
          else:
              return []
  
      def _check_unique(self, **kwargs):
          return [
              checks.Warning(
                  'Setting unique=True on a ForeignKey has the same effect as using a OneToOneField.',
                  hint='ForeignKey(unique=True) is usually better served by a OneToOneField.',
                  obj=self,
                  id='fields.W342',
              )
          ] if self.unique else []
  
      def deconstruct(self):
          name, path, args, kwargs = super().deconstruct()
          del kwargs['to_fields']
          del kwargs['from_fields']
          # Handle the simpler arguments
          if self.db_index:
              del kwargs['db_index']
          else:
              kwargs['db_index'] = False
          if self.db_constraint is not True:
              kwargs['db_constraint'] = self.db_constraint
          # Rel needs more work.
          to_meta = getattr(self.remote_field.model, "_meta", None)
          if self.remote_field.field_name and (
                  not to_meta or (to_meta.pk and self.remote_field.field_name != to_meta.pk.name)):
              kwargs['to_field'] = self.remote_field.field_name
          return name, path, args, kwargs
  
      def to_python(self, value):
          return self.target_field.to_python(value)
  
      @property
      def target_field(self):
          return self.foreign_related_fields[0]
  
      def get_reverse_path_info(self, filtered_relation=None):
          """Get path from the related model to this field's model."""
          opts = self.model._meta
          from_opts = self.remote_field.model._meta
          return [PathInfo(
              from_opts=from_opts,
              to_opts=opts,
              target_fields=(opts.pk,),
              join_field=self.remote_field,
              m2m=not self.unique,
              direct=False,
              filtered_relation=filtered_relation,
          )]
  
      def validate(self, value, model_instance):
          if self.remote_field.parent_link:
              return
          super().validate(value, model_instance)
          if value is None:
              return
  
          using = router.db_for_read(self.remote_field.model, instance=model_instance)
          qs = self.remote_field.model._default_manager.using(using).filter(
              **{self.remote_field.field_name: value}
          )
          qs = qs.complex_filter(self.get_limit_choices_to())
          if not qs.exists():
              raise exceptions.ValidationError(
                  self.error_messages['invalid'],
                  code='invalid',
                  params={
                      'model': self.remote_field.model._meta.verbose_name, 'pk': value,
                      'field': self.remote_field.field_name, 'value': value,
                  },  # 'pk' is included for backwards compatibility
              )
  
      def get_attname(self):
          return '%s_id' % self.name
  
      def get_attname_column(self):
          attname = self.get_attname()
          column = self.db_column or attname
          return attname, column
  
      def get_default(self):
          """Return the to_field if the default value is an object."""
          field_default = super().get_default()
          if isinstance(field_default, self.remote_field.model):
              return getattr(field_default, self.target_field.attname)
          return field_default
  
      def get_db_prep_save(self, value, connection):
          if value is None or (value == '' and
                               (not self.target_field.empty_strings_allowed or
                                connection.features.interprets_empty_strings_as_nulls)):
              return None
          else:
              return self.target_field.get_db_prep_save(value, connection=connection)
  
      def get_db_prep_value(self, value, connection, prepared=False):
          return self.target_field.get_db_prep_value(value, connection, prepared)
  
      def contribute_to_related_class(self, cls, related):
          super().contribute_to_related_class(cls, related)
          if self.remote_field.field_name is None:
              self.remote_field.field_name = cls._meta.pk.name
  
      def formfield(self, *, using=None, **kwargs):
          if isinstance(self.remote_field.model, str):
              raise ValueError("Cannot create form field for %r yet, because "
                               "its related model %r has not been loaded yet" %
                               (self.name, self.remote_field.model))
          return super().formfield(**{
              'form_class': forms.ModelChoiceField,
              'queryset': self.remote_field.model._default_manager.using(using),
              'to_field_name': self.remote_field.field_name,
              **kwargs,
          })
  
      def db_check(self, connection):
          return []
  
      def db_type(self, connection):
          return self.target_field.rel_db_type(connection=connection)
  
      def db_parameters(self, connection):
          return {"type": self.db_type(connection), "check": self.db_check(connection)}
  
      def convert_empty_strings(self, value, expression, connection):
          if (not value) and isinstance(value, str):
              return None
          return value
  
      def get_db_converters(self, connection):
          converters = super().get_db_converters(connection)
          if connection.features.interprets_empty_strings_as_nulls:
              converters += [self.convert_empty_strings]
          return converters
  
      def get_col(self, alias, output_field=None):
          if output_field is None:
              output_field = self.target_field
              while isinstance(output_field, ForeignKey):
                  output_field = output_field.target_field
                  if output_field is self:
                      raise ValueError('Cannot resolve output_field.')
          return super().get_col(alias, output_field)
  
  
  class OneToOneField(ForeignKey):
      """
      A OneToOneField is essentially the same as a ForeignKey, with the exception
      that it always carries a "unique" constraint with it and the reverse
      relation always returns the object pointed to (since there will only ever
      be one), rather than returning a list.
      """
  
      # Field flags
      many_to_many = False
      many_to_one = False
      one_to_many = False
      one_to_one = True
  
      related_accessor_class = ReverseOneToOneDescriptor
      forward_related_accessor_class = ForwardOneToOneDescriptor
      rel_class = OneToOneRel
  
      description = _("One-to-one relationship")
  
      def __init__(self, to, on_delete, to_field=None, **kwargs):
          kwargs['unique'] = True
          super().__init__(to, on_delete, to_field=to_field, **kwargs)
  
      def deconstruct(self):
          name, path, args, kwargs = super().deconstruct()
          if "unique" in kwargs:
              del kwargs['unique']
          return name, path, args, kwargs
  
      def formfield(self, **kwargs):
          if self.remote_field.parent_link:
              return None
          return super().formfield(**kwargs)
  
      def save_form_data(self, instance, data):
          if isinstance(data, self.remote_field.model):
              setattr(instance, self.name, data)
          else:
              setattr(instance, self.attname, data)
  
      def _check_unique(self, **kwargs):
          # Override ForeignKey since check isn't applicable here.
          return []
  
  
  def create_many_to_many_intermediary_model(field, klass):
      from django.db import models
  
      def set_managed(model, related, through):
          through._meta.managed = model._meta.managed or related._meta.managed
  
      to_model = resolve_relation(klass, field.remote_field.model)
      name = '%s_%s' % (klass._meta.object_name, field.name)
      lazy_related_operation(set_managed, klass, to_model, name)
  
      to = make_model_tuple(to_model)[1]
      from_ = klass._meta.model_name
      if to == from_:
          to = 'to_%s' % to
          from_ = 'from_%s' % from_
  
      meta = type('Meta', (), {
          'db_table': field._get_m2m_db_table(klass._meta),
          'auto_created': klass,
          'app_label': klass._meta.app_label,
          'db_tablespace': klass._meta.db_tablespace,
          'unique_together': (from_, to),
          'verbose_name': _('%(from)s-%(to)s relationship') % {'from': from_, 'to': to},
          'verbose_name_plural': _('%(from)s-%(to)s relationships') % {'from': from_, 'to': to},
          'apps': field.model._meta.apps,
      })
      # Construct and return the new class.
      return type(name, (models.Model,), {
          'Meta': meta,
          '__module__': klass.__module__,
          from_: models.ForeignKey(
              klass,
              related_name='%s+' % name,
              db_tablespace=field.db_tablespace,
              db_constraint=field.remote_field.db_constraint,
              on_delete=CASCADE,
          ),
          to: models.ForeignKey(
              to_model,
              related_name='%s+' % name,
              db_tablespace=field.db_tablespace,
              db_constraint=field.remote_field.db_constraint,
              on_delete=CASCADE,
          )
      })
  
  
  class ManyToManyField(RelatedField):
      """
      Provide a many-to-many relation by using an intermediary model that
      holds two ForeignKey fields pointed at the two sides of the relation.
  
      Unless a ``through`` model was provided, ManyToManyField will use the
      create_many_to_many_intermediary_model factory to automatically generate
      the intermediary model.
      """
  
      # Field flags
      many_to_many = True
      many_to_one = False
      one_to_many = False
      one_to_one = False
  
      rel_class = ManyToManyRel
  
      description = _("Many-to-many relationship")
  
      def __init__(self, to, related_name=None, related_query_name=None,
                   limit_choices_to=None, symmetrical=None, through=None,
                   through_fields=None, db_constraint=True, db_table=None,
                   swappable=True, **kwargs):
          try:
              to._meta
          except AttributeError:
              assert isinstance(to, str), (
                  "%s(%r) is invalid. First parameter to ManyToManyField must be "
                  "either a model, a model name, or the string %r" %
                  (self.__class__.__name__, to, RECURSIVE_RELATIONSHIP_CONSTANT)
              )
  
          if symmetrical is None:
              symmetrical = (to == RECURSIVE_RELATIONSHIP_CONSTANT)
  
          if through is not None:
              assert db_table is None, (
                  "Cannot specify a db_table if an intermediary model is used."
              )
  
          kwargs['rel'] = self.rel_class(
              self, to,
              related_name=related_name,
              related_query_name=related_query_name,
              limit_choices_to=limit_choices_to,
              symmetrical=symmetrical,
              through=through,
              through_fields=through_fields,
              db_constraint=db_constraint,
          )
          self.has_null_arg = 'null' in kwargs
  
          super().__init__(**kwargs)
  
          self.db_table = db_table
          self.swappable = swappable
  
      def check(self, **kwargs):
          return [
              *super().check(**kwargs),
              *self._check_unique(**kwargs),
              *self._check_relationship_model(**kwargs),
              *self._check_ignored_options(**kwargs),
              *self._check_table_uniqueness(**kwargs),
          ]
  
      def _check_unique(self, **kwargs):
          if self.unique:
              return [
                  checks.Error(
                      'ManyToManyFields cannot be unique.',
                      obj=self,
                      id='fields.E330',
                  )
              ]
          return []
  
      def _check_ignored_options(self, **kwargs):
          warnings = []
  
          if self.has_null_arg:
              warnings.append(
                  checks.Warning(
                      'null has no effect on ManyToManyField.',
                      obj=self,
                      id='fields.W340',
                  )
              )
  
          if self._validators:
              warnings.append(
                  checks.Warning(
                      'ManyToManyField does not support validators.',
                      obj=self,
                      id='fields.W341',
                  )
              )
          if (self.remote_field.limit_choices_to and self.remote_field.through and
                  not self.remote_field.through._meta.auto_created):
              warnings.append(
                  checks.Warning(
                      'limit_choices_to has no effect on ManyToManyField '
                      'with a through model.',
                      obj=self,
                      id='fields.W343',
                  )
              )
  
          return warnings
  
      def _check_relationship_model(self, from_model=None, **kwargs):
          if hasattr(self.remote_field.through, '_meta'):
              qualified_model_name = "%s.%s" % (
                  self.remote_field.through._meta.app_label, self.remote_field.through.__name__)
          else:
              qualified_model_name = self.remote_field.through
  
          errors = []
  
          if self.remote_field.through not in self.opts.apps.get_models(include_auto_created=True):
              # The relationship model is not installed.
              errors.append(
                  checks.Error(
                      "Field specifies a many-to-many relation through model "
                      "'%s', which has not been installed." % qualified_model_name,
                      obj=self,
                      id='fields.E331',
                  )
              )
  
          else:
              assert from_model is not None, (
                  "ManyToManyField with intermediate "
                  "tables cannot be checked if you don't pass the model "
                  "where the field is attached to."
              )
              # Set some useful local variables
              to_model = resolve_relation(from_model, self.remote_field.model)
              from_model_name = from_model._meta.object_name
              if isinstance(to_model, str):
                  to_model_name = to_model
              else:
                  to_model_name = to_model._meta.object_name
              relationship_model_name = self.remote_field.through._meta.object_name
              self_referential = from_model == to_model
  
              # Check symmetrical attribute.
              if (self_referential and self.remote_field.symmetrical and
                      not self.remote_field.through._meta.auto_created):
                  errors.append(
                      checks.Error(
                          'Many-to-many fields with intermediate tables must not be symmetrical.',
                          obj=self,
                          id='fields.E332',
                      )
                  )
  
              # Count foreign keys in intermediate model
              if self_referential:
                  seen_self = sum(
                      from_model == getattr(field.remote_field, 'model', None)
                      for field in self.remote_field.through._meta.fields
                  )
  
                  if seen_self > 2 and not self.remote_field.through_fields:
                      errors.append(
                          checks.Error(
                              "The model is used as an intermediate model by "
                              "'%s', but it has more than two foreign keys "
                              "to '%s', which is ambiguous. You must specify "
                              "which two foreign keys Django should use via the "
                              "through_fields keyword argument." % (self, from_model_name),
                              hint="Use through_fields to specify which two foreign keys Django should use.",
                              obj=self.remote_field.through,
                              id='fields.E333',
                          )
                      )
  
              else:
                  # Count foreign keys in relationship model
                  seen_from = sum(
                      from_model == getattr(field.remote_field, 'model', None)
                      for field in self.remote_field.through._meta.fields
                  )
                  seen_to = sum(
                      to_model == getattr(field.remote_field, 'model', None)
                      for field in self.remote_field.through._meta.fields
                  )
  
                  if seen_from > 1 and not self.remote_field.through_fields:
                      errors.append(
                          checks.Error(
                              ("The model is used as an intermediate model by "
                               "'%s', but it has more than one foreign key "
                               "from '%s', which is ambiguous. You must specify "
                               "which foreign key Django should use via the "
                               "through_fields keyword argument.") % (self, from_model_name),
                              hint=(
                                  'If you want to create a recursive relationship, '
                                  'use ForeignKey("self", symmetrical=False, through="%s").'
                              ) % relationship_model_name,
                              obj=self,
                              id='fields.E334',
                          )
                      )
  
                  if seen_to > 1 and not self.remote_field.through_fields:
                      errors.append(
                          checks.Error(
                              "The model is used as an intermediate model by "
                              "'%s', but it has more than one foreign key "
                              "to '%s', which is ambiguous. You must specify "
                              "which foreign key Django should use via the "
                              "through_fields keyword argument." % (self, to_model_name),
                              hint=(
                                  'If you want to create a recursive relationship, '
                                  'use ForeignKey("self", symmetrical=False, through="%s").'
                              ) % relationship_model_name,
                              obj=self,
                              id='fields.E335',
                          )
                      )
  
                  if seen_from == 0 or seen_to == 0:
                      errors.append(
                          checks.Error(
                              "The model is used as an intermediate model by "
                              "'%s', but it does not have a foreign key to '%s' or '%s'." % (
                                  self, from_model_name, to_model_name
                              ),
                              obj=self.remote_field.through,
                              id='fields.E336',
                          )
                      )
  
          # Validate `through_fields`.
          if self.remote_field.through_fields is not None:
              # Validate that we're given an iterable of at least two items
              # and that none of them is "falsy".
              if not (len(self.remote_field.through_fields) >= 2 and
                      self.remote_field.through_fields[0] and self.remote_field.through_fields[1]):
                  errors.append(
                      checks.Error(
                          "Field specifies 'through_fields' but does not provide "
                          "the names of the two link fields that should be used "
                          "for the relation through model '%s'." % qualified_model_name,
                          hint="Make sure you specify 'through_fields' as through_fields=('field1', 'field2')",
                          obj=self,
                          id='fields.E337',
                      )
                  )
  
              # Validate the given through fields -- they should be actual
              # fields on the through model, and also be foreign keys to the
              # expected models.
              else:
                  assert from_model is not None, (
                      "ManyToManyField with intermediate "
                      "tables cannot be checked if you don't pass the model "
                      "where the field is attached to."
                  )
  
                  source, through, target = from_model, self.remote_field.through, self.remote_field.model
                  source_field_name, target_field_name = self.remote_field.through_fields[:2]
  
                  for field_name, related_model in ((source_field_name, source),
                                                    (target_field_name, target)):
  
                      possible_field_names = []
                      for f in through._meta.fields:
                          if hasattr(f, 'remote_field') and getattr(f.remote_field, 'model', None) == related_model:
                              possible_field_names.append(f.name)
                      if possible_field_names:
                          hint = "Did you mean one of the following foreign keys to '%s': %s?" % (
                              related_model._meta.object_name,
                              ', '.join(possible_field_names),
                          )
                      else:
                          hint = None
  
                      try:
                          field = through._meta.get_field(field_name)
                      except exceptions.FieldDoesNotExist:
                          errors.append(
                              checks.Error(
                                  "The intermediary model '%s' has no field '%s'."
                                  % (qualified_model_name, field_name),
                                  hint=hint,
                                  obj=self,
                                  id='fields.E338',
                              )
                          )
                      else:
                          if not (hasattr(field, 'remote_field') and
                                  getattr(field.remote_field, 'model', None) == related_model):
                              errors.append(
                                  checks.Error(
                                      "'%s.%s' is not a foreign key to '%s'." % (
                                          through._meta.object_name, field_name,
                                          related_model._meta.object_name,
                                      ),
                                      hint=hint,
                                      obj=self,
                                      id='fields.E339',
                                  )
                              )
  
          return errors
  
      def _check_table_uniqueness(self, **kwargs):
          if isinstance(self.remote_field.through, str) or not self.remote_field.through._meta.managed:
              return []
          registered_tables = {
              model._meta.db_table: model
              for model in self.opts.apps.get_models(include_auto_created=True)
              if model != self.remote_field.through and model._meta.managed
          }
          m2m_db_table = self.m2m_db_table()
          model = registered_tables.get(m2m_db_table)
          # The second condition allows multiple m2m relations on a model if
          # some point to a through model that proxies another through model.
          if model and model._meta.concrete_model != self.remote_field.through._meta.concrete_model:
              if model._meta.auto_created:
                  def _get_field_name(model):
                      for field in model._meta.auto_created._meta.many_to_many:
                          if field.remote_field.through is model:
                              return field.name
                  opts = model._meta.auto_created._meta
                  clashing_obj = '%s.%s' % (opts.label, _get_field_name(model))
              else:
                  clashing_obj = '%s' % model._meta.label
              return [
                  checks.Error(
                      "The field's intermediary table '%s' clashes with the "
                      "table name of '%s'." % (m2m_db_table, clashing_obj),
                      obj=self,
                      id='fields.E340',
                  )
              ]
          return []
  
      def deconstruct(self):
          name, path, args, kwargs = super().deconstruct()
          # Handle the simpler arguments.
          if self.db_table is not None:
              kwargs['db_table'] = self.db_table
          if self.remote_field.db_constraint is not True:
              kwargs['db_constraint'] = self.remote_field.db_constraint
          # Rel needs more work.
          if isinstance(self.remote_field.model, str):
              kwargs['to'] = self.remote_field.model
          else:
              kwargs['to'] = "%s.%s" % (
                  self.remote_field.model._meta.app_label,
                  self.remote_field.model._meta.object_name,
              )
          if getattr(self.remote_field, 'through', None) is not None:
              if isinstance(self.remote_field.through, str):
                  kwargs['through'] = self.remote_field.through
              elif not self.remote_field.through._meta.auto_created:
                  kwargs['through'] = "%s.%s" % (
                      self.remote_field.through._meta.app_label,
                      self.remote_field.through._meta.object_name,
                  )
          # If swappable is True, then see if we're actually pointing to the target
          # of a swap.
          swappable_setting = self.swappable_setting
          if swappable_setting is not None:
              # If it's already a settings reference, error.
              if hasattr(kwargs['to'], "setting_name"):
                  if kwargs['to'].setting_name != swappable_setting:
                      raise ValueError(
                          "Cannot deconstruct a ManyToManyField pointing to a "
                          "model that is swapped in place of more than one model "
                          "(%s and %s)" % (kwargs['to'].setting_name, swappable_setting)
                      )
  
              from django.db.migrations.writer import SettingsReference
              kwargs['to'] = SettingsReference(
                  kwargs['to'],
                  swappable_setting,
              )
          return name, path, args, kwargs
  
      def _get_path_info(self, direct=False, filtered_relation=None):
          """Called by both direct and indirect m2m traversal."""
          int_model = self.remote_field.through
          linkfield1 = int_model._meta.get_field(self.m2m_field_name())
          linkfield2 = int_model._meta.get_field(self.m2m_reverse_field_name())
          if direct:
              join1infos = linkfield1.get_reverse_path_info()
              join2infos = linkfield2.get_path_info(filtered_relation)
          else:
              join1infos = linkfield2.get_reverse_path_info()
              join2infos = linkfield1.get_path_info(filtered_relation)
  
          # Get join infos between the last model of join 1 and the first model
          # of join 2. Assume the only reason these may differ is due to model
          # inheritance.
          join1_final = join1infos[-1].to_opts
          join2_initial = join2infos[0].from_opts
          if join1_final is join2_initial:
              intermediate_infos = []
          elif issubclass(join1_final.model, join2_initial.model):
              intermediate_infos = join1_final.get_path_to_parent(join2_initial.model)
          else:
              intermediate_infos = join2_initial.get_path_from_parent(join1_final.model)
  
          return [*join1infos, *intermediate_infos, *join2infos]
  
      def get_path_info(self, filtered_relation=None):
          return self._get_path_info(direct=True, filtered_relation=filtered_relation)
  
      def get_reverse_path_info(self, filtered_relation=None):
          return self._get_path_info(direct=False, filtered_relation=filtered_relation)
  
      def _get_m2m_db_table(self, opts):
          """
          Function that can be curried to provide the m2m table name for this
          relation.
          """
          if self.remote_field.through is not None:
              return self.remote_field.through._meta.db_table
          elif self.db_table:
              return self.db_table
          else:
              m2m_table_name = '%s_%s' % (utils.strip_quotes(opts.db_table), self.name)
              return utils.truncate_name(m2m_table_name, connection.ops.max_name_length())
  
      def _get_m2m_attr(self, related, attr):
          """
          Function that can be curried to provide the source accessor or DB
          column name for the m2m table.
          """
          cache_attr = '_m2m_%s_cache' % attr
          if hasattr(self, cache_attr):
              return getattr(self, cache_attr)
          if self.remote_field.through_fields is not None:
              link_field_name = self.remote_field.through_fields[0]
          else:
              link_field_name = None
          for f in self.remote_field.through._meta.fields:
              if (f.is_relation and f.remote_field.model == related.related_model and
                      (link_field_name is None or link_field_name == f.name)):
                  setattr(self, cache_attr, getattr(f, attr))
                  return getattr(self, cache_attr)
  
      def _get_m2m_reverse_attr(self, related, attr):
          """
          Function that can be curried to provide the related accessor or DB
          column name for the m2m table.
          """
          cache_attr = '_m2m_reverse_%s_cache' % attr
          if hasattr(self, cache_attr):
              return getattr(self, cache_attr)
          found = False
          if self.remote_field.through_fields is not None:
              link_field_name = self.remote_field.through_fields[1]
          else:
              link_field_name = None
          for f in self.remote_field.through._meta.fields:
              if f.is_relation and f.remote_field.model == related.model:
                  if link_field_name is None and related.related_model == related.model:
                      # If this is an m2m-intermediate to self,
                      # the first foreign key you find will be
                      # the source column. Keep searching for
                      # the second foreign key.
                      if found:
                          setattr(self, cache_attr, getattr(f, attr))
                          break
                      else:
                          found = True
                  elif link_field_name is None or link_field_name == f.name:
                      setattr(self, cache_attr, getattr(f, attr))
                      break
          return getattr(self, cache_attr)
  
      def contribute_to_class(self, cls, name, **kwargs):
          # To support multiple relations to self, it's useful to have a non-None
          # related name on symmetrical relations for internal reasons. The
          # concept doesn't make a lot of sense externally ("you want me to
          # specify *what* on my non-reversible relation?!"), so we set it up
          # automatically. The funky name reduces the chance of an accidental
          # clash.
          if self.remote_field.symmetrical and (
                  self.remote_field.model == "self" or self.remote_field.model == cls._meta.object_name):
              self.remote_field.related_name = "%s_rel_+" % name
          elif self.remote_field.is_hidden():
              # If the backwards relation is disabled, replace the original
              # related_name with one generated from the m2m field name. Django
              # still uses backwards relations internally and we need to avoid
              # clashes between multiple m2m fields with related_name == '+'.
              self.remote_field.related_name = "_%s_%s_+" % (cls.__name__.lower(), name)
  
          super().contribute_to_class(cls, name, **kwargs)
  
          # The intermediate m2m model is not auto created if:
          #  1) There is a manually specified intermediate, or
          #  2) The class owning the m2m field is abstract.
          #  3) The class owning the m2m field has been swapped out.
          if not cls._meta.abstract:
              if self.remote_field.through:
                  def resolve_through_model(_, model, field):
                      field.remote_field.through = model
                  lazy_related_operation(resolve_through_model, cls, self.remote_field.through, field=self)
              elif not cls._meta.swapped:
                  self.remote_field.through = create_many_to_many_intermediary_model(self, cls)
  
          # Add the descriptor for the m2m relation.
          setattr(cls, self.name, ManyToManyDescriptor(self.remote_field, reverse=False))
  
          # Set up the accessor for the m2m table name for the relation.
          self.m2m_db_table = partial(self._get_m2m_db_table, cls._meta)
  
      def contribute_to_related_class(self, cls, related):
          # Internal M2Ms (i.e., those with a related name ending with '+')
          # and swapped models don't get a related descriptor.
          if not self.remote_field.is_hidden() and not related.related_model._meta.swapped:
              setattr(cls, related.get_accessor_name(), ManyToManyDescriptor(self.remote_field, reverse=True))
  
          # Set up the accessors for the column names on the m2m table.
          self.m2m_column_name = partial(self._get_m2m_attr, related, 'column')
          self.m2m_reverse_name = partial(self._get_m2m_reverse_attr, related, 'column')
  
          self.m2m_field_name = partial(self._get_m2m_attr, related, 'name')
          self.m2m_reverse_field_name = partial(self._get_m2m_reverse_attr, related, 'name')
  
          get_m2m_rel = partial(self._get_m2m_attr, related, 'remote_field')
          self.m2m_target_field_name = lambda: get_m2m_rel().field_name
          get_m2m_reverse_rel = partial(self._get_m2m_reverse_attr, related, 'remote_field')
          self.m2m_reverse_target_field_name = lambda: get_m2m_reverse_rel().field_name
  
      def set_attributes_from_rel(self):
          pass
  
      def value_from_object(self, obj):
          return [] if obj.pk is None else list(getattr(obj, self.attname).all())
  
      def save_form_data(self, instance, data):
          getattr(instance, self.attname).set(data)
  
      def formfield(self, *, using=None, **kwargs):
          defaults = {
              'form_class': forms.ModelMultipleChoiceField,
              'queryset': self.remote_field.model._default_manager.using(using),
              **kwargs,
          }
          # If initial is passed in, it's a list of related objects, but the
          # MultipleChoiceField takes a list of IDs.
          if defaults.get('initial') is not None:
              initial = defaults['initial']
              if callable(initial):
                  initial = initial()
              defaults['initial'] = [i.pk for i in initial]
          return super().formfield(**defaults)
  
      def db_check(self, connection):
          return None
  
      def db_type(self, connection):
          # A ManyToManyField is not represented by a single column,
          # so return None.
          return None
  
      def db_parameters(self, connection):
          return {"type": None, "check": None}
  