



'''simple docstring'''





import unittest

import numpy as np
import timeout_decorator  # noqa

from transformers import MarianConfig, is_flax_available
from transformers.testing_utils import require_flax, require_sentencepiece, require_tokenizers, slow
from transformers.utils import cached_property

from ...generation.test_flax_utils import FlaxGenerationTesterMixin
from ...test_modeling_flax_common import FlaxModelTesterMixin, ids_tensor


if is_flax_available():
   import os

   # The slow tests are often failing with OOM error on GPU
   # This makes JAX allocate exactly what is needed on demand, and deallocate memory that is no longer needed
   # but will be slower as stated here https://jax.readthedocs.io/en/latest/gpu_memory_allocation.html
   _UpperCamelCase							    =						'platform'

   import jax
   import jax.numpy as jnp

   from transformers import MarianTokenizer
   from transformers.models.marian.modeling_flax_marian import FlaxMarianModel, FlaxMarianMTModel, shift_tokens_right

def 	a_					(							_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase=None	,_lowerCAmelCase=None	,_lowerCAmelCase=None	,_lowerCAmelCase=None	,_lowerCAmelCase=None	,_lowerCAmelCase=None	,)				->				int:
  if attention_mask is None:
    __lowerCamelCase	:	Tuple   	=			np.where(input_ids != config.pad_token_id	,1	,0	)
  if decoder_attention_mask is None:
    __lowerCamelCase	:	Tuple   	=			np.where(decoder_input_ids != config.pad_token_id	,1	,0	)
  if head_mask is None:
    __lowerCamelCase	:	Union[str, Any]   	=			np.ones((config.encoder_layers, config.encoder_attention_heads)	)
  if decoder_head_mask is None:
    __lowerCamelCase	:	int   	=			np.ones((config.decoder_layers, config.decoder_attention_heads)	)
  if cross_attn_head_mask is None:
    __lowerCamelCase	:	Optional[int]   	=			np.ones((config.decoder_layers, config.decoder_attention_heads)	)
  return {
      "input_ids": input_ids,
      "decoder_input_ids": decoder_input_ids,
      "attention_mask": attention_mask,
      "decoder_attention_mask": attention_mask,
  }






class  lowerCamelCase_   :
  """simple docstring"""




  def __init__(			self				:     Union[str, Any]      ,     _a				:     List[str]      ,     _a				:     List[str]=13      ,     _a				:     Dict=7      ,     _a				:     Union[str, Any]=True      ,     _a				:     int=False      ,     _a				:     int=99      ,     _a				:     Tuple=16      ,     _a				:     Optional[Any]=2      ,     _a				:     Any=4      ,     _a				:     Union[str, Any]=4      ,     _a				:     Any="gelu"      ,     _a				:     Union[str, Any]=0.1      ,     _a				:     List[Any]=0.1      ,     _a				:     Optional[Any]=32      ,     _a				:     Tuple=2      ,     _a				:     int=1      ,     _a				:     Optional[Any]=0      ,     _a				:     Union[str, Any]=0.02      ,     ) -> int:
    __lowerCamelCase	:	Union[str, Any]   	=			parent
    __lowerCamelCase	:	int   	=			batch_size
    __lowerCamelCase	:	Tuple   	=			seq_length
    __lowerCamelCase	:	str   	=			is_training
    __lowerCamelCase	:	Optional[int]   	=			use_labels
    __lowerCamelCase	:	str   	=			vocab_size
    __lowerCamelCase	:	Dict   	=			hidden_size
    __lowerCamelCase	:	int   	=			num_hidden_layers
    __lowerCamelCase	:	List[Any]   	=			num_attention_heads
    __lowerCamelCase	:	Union[str, Any]   	=			intermediate_size
    __lowerCamelCase	:	Tuple   	=			hidden_act
    __lowerCamelCase	:	Any   	=			hidden_dropout_prob
    __lowerCamelCase	:	List[str]   	=			attention_probs_dropout_prob
    __lowerCamelCase	:	Dict   	=			max_position_embeddings
    __lowerCamelCase	:	str   	=			eos_token_id
    __lowerCamelCase	:	Optional[Any]   	=			pad_token_id
    __lowerCamelCase	:	Dict   	=			bos_token_id
    __lowerCamelCase	:	Any   	=			initializer_range




  def 						_lowercase					(			self				:     Tuple       ) -> Dict:
    __lowerCamelCase	:	List[Any]   	=			np.clip(ids_tensor([self.batch_size, self.seq_length - 1]      ,     self.vocab_size       )      ,     3      ,     self.vocab_size       )
    __lowerCamelCase	:	Any   	=			np.concatenate((input_ids, 2 * np.ones((self.batch_size, 1)      ,     dtype=np.intaa       ))      ,     -1       )

    __lowerCamelCase	:	List[str]   	=			shift_tokens_right(__UpperCamelCase      ,     1      ,     2       )

    __lowerCamelCase	:	Optional[int]   	=			MarianConfig(
        vocab_size=self.vocab_size      ,     d_model=self.hidden_size      ,     encoder_layers=self.num_hidden_layers      ,     decoder_layers=self.num_hidden_layers      ,     encoder_attention_heads=self.num_attention_heads      ,     decoder_attention_heads=self.num_attention_heads      ,     encoder_ffn_dim=self.intermediate_size      ,     decoder_ffn_dim=self.intermediate_size      ,     dropout=self.hidden_dropout_prob      ,     attention_dropout=self.attention_probs_dropout_prob      ,     max_position_embeddings=self.max_position_embeddings      ,     eos_token_id=self.eos_token_id      ,     bos_token_id=self.bos_token_id      ,     pad_token_id=self.pad_token_id      ,     initializer_range=self.initializer_range      ,     use_cache=__UpperCamelCase      ,     )
    __lowerCamelCase	:	Any   	=			prepare_marian_inputs_dict(__UpperCamelCase      ,     __UpperCamelCase      ,     __UpperCamelCase       )
    return config, inputs_dict




  def 						_lowercase					(			self				:     Optional[Any]       ) -> Optional[Any]:
    __lowerCamelCase	,__lowerCamelCase	:	Dict   	=			self.prepare_config_and_inputs()
    return config, inputs_dict




  def 						_lowercase					(			self				:     Union[str, Any]      ,     _a				:     Tuple      ,     _a				:     str      ,     _a				:     List[str]       ) -> str:
    __lowerCamelCase	:	Dict   	=			20
    __lowerCamelCase	:	Optional[int]   	=			model_class_name(__UpperCamelCase       )

    __lowerCamelCase	:	Optional[Any]   	=			model.encode(inputs_dict['input_ids']       )

    __lowerCamelCase	,__lowerCamelCase	:	Union[str, Any]   	=			(
        inputs_dict['decoder_input_ids'],
        inputs_dict['decoder_attention_mask'],
    )

    __lowerCamelCase	:	Dict   	=			model.init_cache(decoder_input_ids.shape[0]      ,     __UpperCamelCase      ,     __UpperCamelCase       )
    __lowerCamelCase	:	str   	=			jnp.ones((decoder_input_ids.shape[0], max_decoder_length)      ,     dtype='i4'       )

    __lowerCamelCase	:	List[str]   	=			jnp.broadcast_to(
        jnp.arange(decoder_input_ids.shape[-1] - 1       )[None, :]      ,     (decoder_input_ids.shape[0], decoder_input_ids.shape[-1] - 1)      ,     )
    __lowerCamelCase	:	Optional[int]   	=			model.decode(
        decoder_input_ids[:, :-1]      ,     __UpperCamelCase      ,     decoder_attention_mask=__UpperCamelCase      ,     past_key_values=__UpperCamelCase      ,     decoder_position_ids=__UpperCamelCase      ,     )

    __lowerCamelCase	:	Tuple   	=			jnp.array(decoder_input_ids.shape[0] * [[decoder_input_ids.shape[-1] - 1]]      ,     dtype='i4'       )
    __lowerCamelCase	:	List[Any]   	=			model.decode(
        decoder_input_ids[:, -1:]      ,     __UpperCamelCase      ,     decoder_attention_mask=__UpperCamelCase      ,     past_key_values=outputs_cache.past_key_values      ,     decoder_position_ids=__UpperCamelCase      ,     )

    __lowerCamelCase	:	Dict   	=			model.decode(__UpperCamelCase      ,     __UpperCamelCase       )

    __lowerCamelCase	:	Dict   	=			np.max(np.abs((outputs_cache_next[0][:, -1, :5] - outputs[0][:, -1, :5])       )       )
    self.parent.assertTrue(diff < 1e-3      ,     msg=f'Max diff is {diff}'       )




  def 						_lowercase					(			self				:     Union[str, Any]      ,     _a				:     str      ,     _a				:     Dict      ,     _a				:     Tuple       ) -> Dict:
    __lowerCamelCase	:	Union[str, Any]   	=			20
    __lowerCamelCase	:	Any   	=			model_class_name(__UpperCamelCase       )

    __lowerCamelCase	:	Optional[Any]   	=			model.encode(inputs_dict['input_ids']       )

    __lowerCamelCase	,__lowerCamelCase	:	List[Any]   	=			(
        inputs_dict['decoder_input_ids'],
        inputs_dict['decoder_attention_mask'],
    )

    __lowerCamelCase	:	Dict   	=			jnp.concatenate(
        [
            decoder_attention_mask,
            jnp.zeros((decoder_attention_mask.shape[0], max_decoder_length - decoder_attention_mask.shape[1])       ),
        ]      ,     axis=-1      ,     )

    __lowerCamelCase	:	List[str]   	=			model.init_cache(decoder_input_ids.shape[0]      ,     __UpperCamelCase      ,     __UpperCamelCase       )
    __lowerCamelCase	:	Optional[int]   	=			jnp.broadcast_to(
        jnp.arange(decoder_input_ids.shape[-1] - 1       )[None, :]      ,     (decoder_input_ids.shape[0], decoder_input_ids.shape[-1] - 1)      ,     )

    __lowerCamelCase	:	Tuple   	=			model.decode(
        decoder_input_ids[:, :-1]      ,     __UpperCamelCase      ,     decoder_attention_mask=__UpperCamelCase      ,     past_key_values=__UpperCamelCase      ,     decoder_position_ids=__UpperCamelCase      ,     )
    __lowerCamelCase	:	Optional[int]   	=			jnp.array(decoder_input_ids.shape[0] * [[decoder_input_ids.shape[-1] - 1]]      ,     dtype='i4'       )
    __lowerCamelCase	:	int   	=			model.decode(
        decoder_input_ids[:, -1:]      ,     __UpperCamelCase      ,     past_key_values=outputs_cache.past_key_values      ,     decoder_attention_mask=__UpperCamelCase      ,     decoder_position_ids=__UpperCamelCase      ,     )

    __lowerCamelCase	:	Union[str, Any]   	=			model.decode(__UpperCamelCase      ,     __UpperCamelCase      ,     decoder_attention_mask=__UpperCamelCase       )

    __lowerCamelCase	:	List[str]   	=			np.max(np.abs((outputs_cache_next[0][:, -1, :5] - outputs[0][:, -1, :5])       )       )
    self.parent.assertTrue(diff < 1e-3      ,     msg=f'Max diff is {diff}'       )






@require_flax
class  lowerCamelCase_   (    lowercase_       ,       unittest.TestCase       ,       lowercase_					):
  """simple docstring"""




  a_							 =True
  a_							 =(FlaxMarianModel, FlaxMarianMTModel) if is_flax_available() else ()
  a_							 =(FlaxMarianMTModel,) if is_flax_available() else ()




  def 						_lowercase					(			self				:     Dict       ) -> Optional[int]:
    __lowerCamelCase	:	int   	=			FlaxMarianModelTester(self       )




  def 						_lowercase					(			self				:     str       ) -> List[str]:
    __lowerCamelCase	,__lowerCamelCase	:	Optional[Any]   	=			self.model_tester.prepare_config_and_inputs()
    for model_class in self.all_model_classes:
      self.model_tester.check_use_cache_forward(__UpperCamelCase      ,     __UpperCamelCase      ,     __UpperCamelCase       )




  def 						_lowercase					(			self				:     Dict       ) -> List[Any]:
    __lowerCamelCase	,__lowerCamelCase	:	Tuple   	=			self.model_tester.prepare_config_and_inputs()
    for model_class in self.all_model_classes:
      self.model_tester.check_use_cache_forward_with_attn_mask(__UpperCamelCase      ,     __UpperCamelCase      ,     __UpperCamelCase       )




  def 						_lowercase					(			self				:     int       ) -> Union[str, Any]:
    __lowerCamelCase	,__lowerCamelCase	:	str   	=			self.model_tester.prepare_config_and_inputs_for_common()

    for model_class in self.all_model_classes:
      with self.subTest(model_class.__name__       ):
        __lowerCamelCase	:	Tuple   	=			self._prepare_for_class(__UpperCamelCase      ,     __UpperCamelCase       )
        __lowerCamelCase	:	List[str]   	=			model_class(__UpperCamelCase       )

        @jax.jit
        def encode_jitted(_a				:     Optional[int]      ,     _a				:     Dict=None      ,     **_a				:     List[Any]       ):
          return model.encode(input_ids=__UpperCamelCase      ,     attention_mask=__UpperCamelCase       )

        with self.subTest('JIT Enabled'       ):
          __lowerCamelCase	:	Dict   	=			encode_jitted(**__UpperCamelCase       ).to_tuple()

        with self.subTest('JIT Disabled'       ):
          with jax.disable_jit():
            __lowerCamelCase	:	Tuple   	=			encode_jitted(**__UpperCamelCase       ).to_tuple()

        self.assertEqual(len(__UpperCamelCase       )      ,     len(__UpperCamelCase       )       )
        for jitted_output, output in zip(__UpperCamelCase      ,     __UpperCamelCase       ):
          self.assertEqual(jitted_output.shape      ,     output.shape       )




  def 						_lowercase					(			self				:     Optional[int]       ) -> str:
    __lowerCamelCase	,__lowerCamelCase	:	Tuple   	=			self.model_tester.prepare_config_and_inputs_for_common()

    for model_class in self.all_model_classes:
      with self.subTest(model_class.__name__       ):
        __lowerCamelCase	:	int   	=			model_class(__UpperCamelCase       )
        __lowerCamelCase	:	Union[str, Any]   	=			model.encode(inputs_dict['input_ids']      ,     inputs_dict['attention_mask']       )

        __lowerCamelCase	:	Any   	=			{
            'decoder_input_ids': inputs_dict['decoder_input_ids'],
            'decoder_attention_mask': inputs_dict['decoder_attention_mask'],
            'encoder_outputs': encoder_outputs,
        }

        @jax.jit
        def decode_jitted(_a				:     Optional[Any]      ,     _a				:     Optional[Any]      ,     _a				:     List[str]       ):
          return model.decode(
              decoder_input_ids=__UpperCamelCase      ,     decoder_attention_mask=__UpperCamelCase      ,     encoder_outputs=__UpperCamelCase      ,     )

        with self.subTest('JIT Enabled'       ):
          __lowerCamelCase	:	List[str]   	=			decode_jitted(**__UpperCamelCase       ).to_tuple()

        with self.subTest('JIT Disabled'       ):
          with jax.disable_jit():
            __lowerCamelCase	:	List[str]   	=			decode_jitted(**__UpperCamelCase       ).to_tuple()

        self.assertEqual(len(__UpperCamelCase       )      ,     len(__UpperCamelCase       )       )
        for jitted_output, output in zip(__UpperCamelCase      ,     __UpperCamelCase       ):
          self.assertEqual(jitted_output.shape      ,     output.shape       )




  @slow
  def 						_lowercase					(			self				:     str       ) -> int:
    for model_class_name in self.all_model_classes:
      __lowerCamelCase	:	Union[str, Any]   	=			model_class_name.from_pretrained('Helsinki-NLP/opus-mt-en-de'       )
      # FlaxMarianForSequenceClassification expects eos token in input_ids
      __lowerCamelCase	:	Dict   	=			np.ones((1, 1)       ) * model.config.eos_token_id
      __lowerCamelCase	:	Union[str, Any]   	=			model(__UpperCamelCase       )
      self.assertIsNotNone(__UpperCamelCase       )






@require_flax
@require_sentencepiece
@require_tokenizers
class  lowerCamelCase_   (    unittest.TestCase					):
  """simple docstring"""




  a_							 =None
  a_							 =None




  @classmethod
  def 						_lowercase					(			cls				:     Tuple       ) -> str:
    __lowerCamelCase	:	Optional[int]   	=			f'Helsinki-NLP/opus-mt-{cls.src}-{cls.tgt}'
    return cls




  @cached_property
  def 						_lowercase					(			self				:     Optional[int]       ) -> Optional[int]:
    return MarianTokenizer.from_pretrained(self.model_name       )




  @property
  def 						_lowercase					(			self				:     int       ) -> List[str]:
    return self.tokenizer.eos_token_id




  @cached_property
  def 						_lowercase					(			self				:     List[Any]       ) -> List[Any]:
    __lowerCamelCase	:	int   	=			FlaxMarianMTModel.from_pretrained(self.model_name       )
    self.assertEqual(model.config.decoder_start_token_id      ,     model.config.pad_token_id       )
    return model




  def 						_lowercase					(			self				:     int      ,     **_a				:     List[str]       ) -> Any:
    __lowerCamelCase	:	Optional[int]   	=			self.translate_src_text(**__UpperCamelCase       )
    self.assertListEqual(self.expected_text      ,     __UpperCamelCase       )




  def 						_lowercase					(			self				:     List[Any]      ,     **_a				:     List[Any]       ) -> str:
    __lowerCamelCase	:	Tuple   	=			self.tokenizer(self.src_text      ,     padding=__UpperCamelCase      ,     return_tensors='np'      ,     **__UpperCamelCase       )
    __lowerCamelCase	:	Any   	=			self.model.generate(
        model_inputs.input_ids      ,     attention_mask=model_inputs.attention_mask      ,     num_beams=2      ,     max_length=128      ,     ).sequences
    __lowerCamelCase	:	Dict   	=			self.tokenizer.batch_decode(__UpperCamelCase      ,     skip_special_tokens=__UpperCamelCase       )
    return generated_words






@require_flax
@require_sentencepiece
@require_tokenizers
class  lowerCamelCase_   (    lowercase_					):
  """simple docstring"""




  a_							 ="""en"""
  a_							 ="""fr"""
  a_							 =[
      """I am a small frog.""",
      """Now I can forget the 100 words of german that I know.""",
  ]
  a_							 =[
      """Je suis une petite grenouille.""",
      """Maintenant, je peux oublier les 100 mots d\'allemand que je connais.""",
  ]




  @slow
  def 						_lowercase					(			self				:     str       ) -> Any:
    self._assert_generated_batch_equal_expected()






@require_flax
@require_sentencepiece
@require_tokenizers
class  lowerCamelCase_   (    lowercase_					):
  """simple docstring"""




  a_							 ="""fr"""
  a_							 ="""en"""
  a_							 =[
      """Donnez moi le micro.""",
      """Tom et Mary étaient assis à une table.""",  # Accents
  ]
  a_							 =[
      """Give me the microphone.""",
      """Tom and Mary were sitting at a table.""",
  ]




  @slow
  def 						_lowercase					(			self				:     Optional[Any]       ) -> int:
    self._assert_generated_batch_equal_expected()






@require_flax
@require_sentencepiece
@require_tokenizers
class  lowerCamelCase_   (    lowercase_					):
  """simple docstring"""




  a_							 ="""mt"""
  a_							 ="""en"""
  a_							 =["""Billi messu b\'mod ġentili, Ġesù fejjaq raġel li kien milqut bil - marda kerha tal - ġdiem."""]
  a_							 =["""Touching gently, Jesus healed a man who was affected by the sad disease of leprosy."""]




  @slow
  def 						_lowercase					(			self				:     Optional[int]       ) -> Tuple:
    self._assert_generated_batch_equal_expected()






@require_flax
@require_sentencepiece
@require_tokenizers
class  lowerCamelCase_   (    lowercase_					):
  """simple docstring"""




  a_							 ="""en"""
  a_							 ="""de"""
  a_							 =[
      """I am a small frog.""",
      """Now I can forget the 100 words of german that I know.""",
      """Tom asked his teacher for advice.""",
      """That\'s how I would do it.""",
      """Tom really admired Mary\'s courage.""",
      """Turn around and close your eyes.""",
  ]
  a_							 =[
      """Ich bin ein kleiner Frosch.""",
      """Jetzt kann ich die 100 Wörter des Deutschen vergessen, die ich kenne.""",
      """Tom bat seinen Lehrer um Rat.""",
      """So würde ich das machen.""",
      """Tom bewunderte Marias Mut wirklich.""",
      """Drehen Sie sich um und schließen Sie die Augen.""",
  ]




  @slow
  def 						_lowercase					(			self				:     Any       ) -> List[Any]:
    self._assert_generated_batch_equal_expected()






@require_flax
@require_sentencepiece
@require_tokenizers
class  lowerCamelCase_   (    lowercase_					):
  """simple docstring"""




  a_							 ="""en"""
  a_							 ="""zh"""
  a_							 =["""My name is Wolfgang and I live in Berlin"""]
  a_							 =["""我叫沃尔夫冈 我住在柏林"""]




  @slow
  def 						_lowercase					(			self				:     List[str]       ) -> Tuple:
    self._assert_generated_batch_equal_expected()






@require_flax
@require_sentencepiece
@require_tokenizers
class  lowerCamelCase_   (    lowercase_					):
  """simple docstring"""




  a_							 ="""ru"""
  a_							 ="""fr"""
  a_							 =["""Он показал мне рукопись своей новой пьесы."""]
  a_							 =["""Il m\'a montré le manuscrit de sa nouvelle pièce."""]




  @slow
  def 						_lowercase					(			self				:     Any       ) -> Union[str, Any]:
    self._assert_generated_batch_equal_expected()






@require_flax
@require_sentencepiece
@require_tokenizers
class  lowerCamelCase_   (    lowercase_					):
  """simple docstring"""




  a_							 ="""en"""
  a_							 ="""ROMANCE"""
  a_							 =[
      """>>fr<< Don\'t spend so much time watching TV.""",
      """>>pt<< Your message has been sent.""",
      """>>es<< He\'s two years older than me.""",
  ]
  a_							 =[
      """Ne passez pas autant de temps à regarder la télé.""",
      """A sua mensagem foi enviada.""",
      """Es dos años más viejo que yo.""",
  ]




  @slow
  def 						_lowercase					(			self				:     Optional[int]       ) -> Optional[Any]:
    self._assert_generated_batch_equal_expected()











'''simple docstring'''





from __future__ import annotations

from collections.abc import Iterable






class  lowerCamelCase_   :
  """simple docstring"""




  def __init__(			self				:     int      ,     _a				:     Dict      ,     _a				:     Optional[Any]       ) -> str:
    __lowerCamelCase	,__lowerCamelCase	:	List[Any]   	=			float(_a       ), float(_a       )




  def __eq__(			self				:     Tuple      ,     _a				:     List[Any]       ) -> Optional[int]:
    return self.x == other.x and self.y == other.y




  def __ne__(			self				:     Tuple      ,     _a				:     Optional[int]       ) -> List[str]:
    return not self == other




  def __gt__(			self				:     Tuple      ,     _a				:     str       ) -> str:
    if self.x > other.x:
      return True
    elif self.x == other.x:
      return self.y > other.y
    return False




  def __lt__(			self				:     Union[str, Any]      ,     _a				:     List[Any]       ) -> Optional[Any]:
    return not self > other




  def __ge__(			self				:     Tuple      ,     _a				:     Optional[Any]       ) -> Optional[int]:
    if self.x > other.x:
      return True
    elif self.x == other.x:
      return self.y >= other.y
    return False




  def __le__(			self				:     Any      ,     _a				:     List[str]       ) -> Optional[int]:
    if self.x < other.x:
      return True
    elif self.x == other.x:
      return self.y <= other.y
    return False




  def __repr__(			self				:     int       ) -> Optional[int]:
    return f'({self.x}, {self.y})'




  def __hash__(			self				:     Optional[Any]       ) -> Union[str, Any]:
    return hash(self.x       )




def 	a_					(							_lowerCAmelCase	,)				->				list[Point]:
  __lowerCamelCase	:	list[Point]   	=			[]
  if list_of_tuples:
    for p in list_of_tuples:
      if isinstance(_lowerCAmelCase	,_lowerCAmelCase	):
        points.append(_lowerCAmelCase	)
      else:
        try:
          points.append(Point(p[0]	,p[1]	)	)
        except (IndexError, TypeError):
          print(
              F'Ignoring deformed point {p}. All points'
              ' must have at least 2 coordinates.'	)
  return points

def 	a_					(							_lowerCAmelCase	)				->				list[Point]:

  if not hasattr(_lowerCAmelCase	,'__iter__'	):
    __lowerCamelCase	:	str   	=			F'Expecting an iterable object but got an non-iterable type {points}'
    raise ValueError(_lowerCAmelCase	)

  if not points:
    __lowerCamelCase	:	Any   	=			F'Expecting a list of points but got {points}'
    raise ValueError(_lowerCAmelCase	)

  return _construct_points(_lowerCAmelCase	)

def 	a_					(							_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	)				->				float:
  __lowerCamelCase	:	Optional[int]   	=			(a.x * b.y + b.x * c.y + c.x * a.y) - (a.y * b.x + b.y * c.x + c.y * a.x)
  return det

def 	a_					(							_lowerCAmelCase	)				->				list[Point]:
  __lowerCamelCase	:	Optional[Any]   	=			sorted(_validate_input(_lowerCAmelCase	)	)
  __lowerCamelCase	:	Optional[int]   	=			len(_lowerCAmelCase	)
  __lowerCamelCase	:	Union[str, Any]   	=			set()

  for i in range(n - 1	):
    for j in range(i + 1	,_lowerCAmelCase	):
      __lowerCamelCase	:	List[Any]   	=			False
      __lowerCamelCase	:	Union[str, Any]   	=			True
      for k in range(_lowerCAmelCase	):
        if k != i and k != j:
          __lowerCamelCase	:	Any   	=			_det(points[i]	,points[j]	,points[k]	)

          if det_k > 0:
            __lowerCamelCase	:	List[Any]   	=			True
          elif det_k < 0:
            __lowerCamelCase	:	Any   	=			True
          else:
            # point[i], point[j], point[k] all lie on a straight line
            # if point[k] is to the left of point[i] or it's to the
            # right of point[j], then point[i], point[j] cannot be
            # part of the convex hull of A
            if points[k] < points[i] or points[k] > points[j]:
              __lowerCamelCase	:	Dict   	=			False
              break

        if points_left_of_ij and points_right_of_ij:
          __lowerCamelCase	:	int   	=			False
          break

      if ij_part_of_convex_hull:
        convex_set.update([points[i], points[j]]	)

  return sorted(_lowerCAmelCase	)

def 	a_					(							_lowerCAmelCase	)				->				list[Point]:
  __lowerCamelCase	:	Dict   	=			sorted(_validate_input(_lowerCAmelCase	)	)
  __lowerCamelCase	:	Optional[Any]   	=			len(_lowerCAmelCase	)

  # divide all the points into an upper hull and a lower hull
  # the left most point and the right most point are definitely
  # members of the convex hull by definition.
  # use these two anchors to divide all the points into two hulls,
  # an upper hull and a lower hull.

  # all points to the left (above) the line joining the extreme points belong to the
  # upper hull
  # all points to the right (below) the line joining the extreme points below to the
  # lower hull
  # ignore all points on the line joining the extreme points since they cannot be
  # part of the convex hull

  __lowerCamelCase	:	str   	=			points[0]
  __lowerCamelCase	:	Optional[Any]   	=			points[n - 1]

  __lowerCamelCase	:	Tuple   	=			{left_most_point, right_most_point}
  __lowerCamelCase	:	int   	=			[]
  __lowerCamelCase	:	Tuple   	=			[]

  for i in range(1	,n - 1	):
    __lowerCamelCase	:	Dict   	=			_det(_lowerCAmelCase	,_lowerCAmelCase	,points[i]	)

    if det > 0:
      upper_hull.append(points[i]	)
    elif det < 0:
      lower_hull.append(points[i]	)

  _construct_hull(_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	)
  _construct_hull(_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	)

  return sorted(_lowerCAmelCase	)

def 	a_					(							_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	)				->				None:
  if points:
    __lowerCamelCase	:	Optional[int]   	=			None
    __lowerCamelCase	:	Optional[Any]   	=			float('-inf'	)
    __lowerCamelCase	:	Optional[int]   	=			[]

    for p in points:
      __lowerCamelCase	:	List[str]   	=			_det(_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	)

      if det > 0:
        candidate_points.append(_lowerCAmelCase	)

        if det > extreme_point_distance:
          __lowerCamelCase	:	Union[str, Any]   	=			det
          __lowerCamelCase	:	Dict   	=			p

    if extreme_point:
      _construct_hull(_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	)
      convex_set.add(_lowerCAmelCase	)
      _construct_hull(_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	)

def 	a_					(							_lowerCAmelCase	)				->				list[Point]:
  __lowerCamelCase	:	Optional[int]   	=			sorted(_validate_input(_lowerCAmelCase	)	)
  __lowerCamelCase	:	List[Any]   	=			len(_lowerCAmelCase	)

  __lowerCamelCase	:	Tuple   	=			points[:2]
  for i in range(2	,_lowerCAmelCase	):
    __lowerCamelCase	:	Tuple   	=			_det(convex_hull[1]	,convex_hull[0]	,points[i]	)
    if det > 0:
      convex_hull.insert(0	,points[i]	)
      break
    elif det < 0:
      convex_hull.append(points[i]	)
      break
    else:
      __lowerCamelCase	:	Optional[int]   	=			points[i]
  i += 1

  for j in range(_lowerCAmelCase	,_lowerCAmelCase	):
    if (
        _det(convex_hull[0]	,convex_hull[-1]	,points[j]	) > 0
        and _det(convex_hull[-1]	,convex_hull[0]	,points[1]	) < 0
    ):
      # The point lies within the convex hull
      continue

    convex_hull.insert(0	,points[j]	)
    convex_hull.append(points[j]	)
    while _det(convex_hull[0]	,convex_hull[1]	,convex_hull[2]	) >= 0:
      del convex_hull[1]
    while _det(convex_hull[-1]	,convex_hull[-2]	,convex_hull[-3]	) <= 0:
      del convex_hull[-2]

    # `convex_hull` is contains the convex hull in circular order
  return sorted(convex_hull[1:] if len(_lowerCAmelCase	) > 3 else convex_hull	)

def 	a_					(							)				->				Optional[int]:
  __lowerCamelCase	:	List[Any]   	=			[
      (0, 3),
      (2, 2),
      (1, 1),
      (2, 1),
      (3, 0),
      (0, 0),
      (3, 3),
      (2, -1),
      (2, -4),
      (1, -3),
  ]
  # the convex set of points is
  # [(0, 0), (0, 3), (1, -3), (2, -4), (3, 0), (3, 3)]
  __lowerCamelCase	:	Any   	=			convex_hull_bf(_lowerCAmelCase	)

  __lowerCamelCase	:	Optional[int]   	=			convex_hull_recursive(_lowerCAmelCase	)
  assert results_bf == results_recursive

  __lowerCamelCase	:	int   	=			convex_hull_melkman(_lowerCAmelCase	)
  assert results_bf == results_melkman

  print(_lowerCAmelCase	)


if __name__ == "__main__":
   main()






