




from __future__ import annotations

from collections.abc import Iterable


class     __SCREAMING_SNAKE_CASE							:

     def __init__(    self			,	__lowercase			,	__lowercase ):







      '''simple docstring'''




      lowerCamelCase_							:		Optional[int]							       =							float(__lowercase ), float(__lowercase )

     def __eq__(    self			,	__lowercase ):







      '''simple docstring'''




      return self.x == other.x and self.y == other.y

     def __ne__(    self			,	__lowercase ):







      '''simple docstring'''




      return not self == other

     def __gt__(    self			,	__lowercase ):







      '''simple docstring'''




      if self.x > other.x:
       return True
      elif self.x == other.x:
       return self.y > other.y
      return False

     def __lt__(    self			,	__lowercase ):







      '''simple docstring'''




      return not self > other

     def __ge__(    self			,	__lowercase ):







      '''simple docstring'''




      if self.x > other.x:
       return True
      elif self.x == other.x:
       return self.y >= other.y
      return False

     def __le__(    self			,	__lowercase ):







      '''simple docstring'''




      if self.x < other.x:
       return True
      elif self.x == other.x:
       return self.y <= other.y
      return False

     def __repr__(    self ):







      '''simple docstring'''




      return f"({self.x}, {self.y})"





     def __hash__(    self ):







      '''simple docstring'''




      return hash(self.x )






def  snake_case (							A						,       )							->							list[Point]:




 '''simple docstring'''


 lowerCamelCase_							:		list[Point]							       =							[]
 if list_of_tuples:
  for p in list_of_tuples:
   if isinstance(A						,       A      ):
    points.append(A      )
   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  snake_case (							A      )							->							list[Point]:




 '''simple docstring'''


 if not hasattr(A						,       '__iter__'      ):
  lowerCamelCase_							:		List[Any]							       =							f"Expecting an iterable object but got an non-iterable type {points}"
  raise ValueError(A      )

 if not points:
  lowerCamelCase_							:		str							       =							f"Expecting a list of points but got {points}"
  raise ValueError(A      )

 return _construct_points(A      )






def  snake_case (							A						,       A						,       A      )							->							float:




 '''simple docstring'''


 lowerCamelCase_							:		str							       =							(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  snake_case (							A      )							->							list[Point]:




 '''simple docstring'''


 lowerCamelCase_							:		Dict							       =							sorted(_validate_input(A      )      )
 lowerCamelCase_							:		List[Any]							       =							len(A      )
 lowerCamelCase_							:		Optional[int]							       =							set()

 for i in range(n - 1      ):
  for j in range(i + 1						,       A      ):
   lowerCamelCase_							:		Tuple							       =							False
   lowerCamelCase_							:		Any							       =							True
   for k in range(A      ):
    if k != i and k != j:
     lowerCamelCase_							:		str							       =							_det(points[i]						,       points[j]						,       points[k]      )

     if det_k > 0:
      lowerCamelCase_							:		Any							       =							True
     elif det_k < 0:
      lowerCamelCase_							:		Optional[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_							:		List[Any]							       =							False
       break

    if points_left_of_ij and points_right_of_ij:
     lowerCamelCase_							:		List[Any]							       =							False
     break

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

 return sorted(A      )






def  snake_case (							A      )							->							list[Point]:




 '''simple docstring'''


 lowerCamelCase_							:		List[str]							       =							sorted(_validate_input(A      )      )
 lowerCamelCase_							:		Optional[Any]							       =							len(A      )

 # 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_							:		Optional[int]							       =							points[0]
 lowerCamelCase_							:		Optional[Any]							       =							points[n - 1]

 lowerCamelCase_							:		List[str]							       =							{left_most_point, right_most_point}
 lowerCamelCase_							:		List[str]							       =							[]
 lowerCamelCase_							:		Any							       =							[]

 for i in range(1						,       n - 1      ):
  lowerCamelCase_							:		List[str]							       =							_det(A						,       A						,       points[i]      )

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

 _construct_hull(A						,       A						,       A						,       A      )
 _construct_hull(A						,       A						,       A						,       A      )

 return sorted(A      )






def  snake_case (							A						,       A						,       A						,       A      )							->							None:




 '''simple docstring'''


 if points:
  lowerCamelCase_							:		Any							       =							None
  lowerCamelCase_							:		List[Any]							       =							float('-inf'      )
  lowerCamelCase_							:		Any							       =							[]

  for p in points:
   lowerCamelCase_							:		int							       =							_det(A						,       A						,       A      )

   if det > 0:
    candidate_points.append(A      )

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

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






def  snake_case (							A      )							->							list[Point]:




 '''simple docstring'''


 lowerCamelCase_							:		int							       =							sorted(_validate_input(A      )      )
 lowerCamelCase_							:		List[str]							       =							len(A      )

 lowerCamelCase_							:		List[Any]							       =							points[:2]
 for i in range(2						,       A      ):
  lowerCamelCase_							:		int							       =							_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_							:		Dict							       =							points[i]
 i += 1

 for j in range(A						,       A      ):
  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(A      ) > 3 else convex_hull      )






def  snake_case (							)							->							Optional[int]:




 '''simple docstring'''


 lowerCamelCase_							:		Union[str, 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_							:		Union[str, Any]							       =							convex_hull_bf(A      )

 lowerCamelCase_							:		Any							       =							convex_hull_recursive(A      )
 assert results_bf == results_recursive

 lowerCamelCase_							:		Any							       =							convex_hull_melkman(A      )
 assert results_bf == results_melkman

 print(A      )


if __name__ == "__main__":
       main()






from collections import OrderedDict
from typing import Any, Mapping, Optional

from ... import PreTrainedTokenizer
from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig, OnnxSeqaSeqConfigWithPast
from ...onnx.utils import compute_effective_axis_dimension
from ...utils import TensorType, is_torch_available, logging


UpperCamelCase__		=						logging.get_logger(__name__)

UpperCamelCase__		=						{
    'facebook/m2m100_418M': 'https://huggingface.co/facebook/m2m100_418M/resolve/main/config.json',
    # See all M2M100 models at https://huggingface.co/models?filter=m2m_100
}


class     __SCREAMING_SNAKE_CASE							(		lowerCamelCase  ):
					_lowerCamelCase		  =			"""m2m_100"""
					_lowerCamelCase		  =			["""past_key_values"""]
					_lowerCamelCase		  =			{"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}

					def __init__(    self			,	__lowercase=128_112			,	__lowercase=1_024			,	__lowercase=12			,	__lowercase=4_096			,	__lowercase=16			,	__lowercase=12			,	__lowercase=4_096			,	__lowercase=16			,	__lowercase=0.05			,	__lowercase=0.05			,	__lowercase=True			,	__lowercase=True			,	__lowercase="relu"			,	__lowercase=1_024			,	__lowercase=0.1			,	__lowercase=0.1			,	__lowercase=0.0			,	__lowercase=0.02			,	__lowercase=2			,	__lowercase=True			,	__lowercase=1			,	__lowercase=0			,	__lowercase=2			,	**__lowercase			,	):







						'''simple docstring'''




						lowerCamelCase_							:		int							       =							vocab_size
						lowerCamelCase_							:		List[str]							       =							max_position_embeddings
						lowerCamelCase_							:		Tuple							       =							d_model
						lowerCamelCase_							:		Optional[int]							       =							encoder_ffn_dim
						lowerCamelCase_							:		Union[str, Any]							       =							encoder_layers
						lowerCamelCase_							:		Dict							       =							encoder_attention_heads
						lowerCamelCase_							:		Union[str, Any]							       =							decoder_ffn_dim
						lowerCamelCase_							:		List[str]							       =							decoder_layers
						lowerCamelCase_							:		Union[str, Any]							       =							decoder_attention_heads
						lowerCamelCase_							:		Optional[int]							       =							dropout
						lowerCamelCase_							:		str							       =							attention_dropout
						lowerCamelCase_							:		Optional[Any]							       =							activation_dropout
						lowerCamelCase_							:		str							       =							activation_function
						lowerCamelCase_							:		int							       =							init_std
						lowerCamelCase_							:		Optional[int]							       =							encoder_layerdrop
						lowerCamelCase_							:		Tuple							       =							decoder_layerdrop
						lowerCamelCase_							:		Tuple							       =							use_cache
						lowerCamelCase_							:		Any							       =							encoder_layers
						lowerCamelCase_							:		Any							       =							scale_embedding  # scale factor will be sqrt(d_model) if True

						super().__init__(
						    pad_token_id=__lowercase			,	bos_token_id=__lowercase			,	eos_token_id=__lowercase			,	is_encoder_decoder=__lowercase			,	decoder_start_token_id=__lowercase			,	**__lowercase			,	)


class     __SCREAMING_SNAKE_CASE							(		lowerCamelCase  ):

					@property
					def      lowercase_							(    self ):







						'''simple docstring'''




						lowerCamelCase_							:		Any							       =							OrderedDict(
						    [
						        ('input_ids', {0: 'batch', 1: 'encoder_sequence'}),
						        ('attention_mask', {0: 'batch', 1: 'encoder_sequence'}),
						    ] )

						if self.use_past:
							lowerCamelCase_							:		Union[str, Any]							       =							{0: 'batch'}
							lowerCamelCase_							:		Optional[Any]							       =							{0: 'batch', 1: 'past_decoder_sequence + sequence'}
						else:
							lowerCamelCase_							:		Any							       =							{0: 'batch', 1: 'decoder_sequence'}
							lowerCamelCase_							:		Union[str, Any]							       =							{0: 'batch', 1: 'decoder_sequence'}

						if self.use_past:
							self.fill_with_past_key_values_(__lowercase			,	direction='inputs' )
						return common_inputs

					def      lowercase_							(    self			,	__lowercase			,	__lowercase = -1			,	__lowercase = -1			,	__lowercase = False			,	__lowercase = None			,	):







						'''simple docstring'''




						lowerCamelCase_							:		Optional[int]							       =							compute_effective_axis_dimension(
						    __lowercase			,	fixed_dimension=OnnxConfig.default_fixed_batch			,	num_token_to_add=0 )

						# If dynamic axis (-1) we forward with a fixed dimension of 8 tokens to avoid optimizations made by ONNX
						lowerCamelCase_							:		str							       =							tokenizer.num_special_tokens_to_add(__lowercase )
						lowerCamelCase_							:		Dict							       =							compute_effective_axis_dimension(
						    __lowercase			,	fixed_dimension=OnnxConfig.default_fixed_sequence			,	num_token_to_add=__lowercase )

						# Generate dummy inputs according to compute batch and sequence
						lowerCamelCase_							:		Optional[int]							       =							[' '.join([tokenizer.unk_token] ) * seq_length] * batch_size
						lowerCamelCase_							:		Optional[Any]							       =							dict(tokenizer(__lowercase			,	return_tensors=__lowercase ) )
						return common_inputs

					def      lowercase_							(    self			,	__lowercase			,	__lowercase = -1			,	__lowercase = -1			,	__lowercase = False			,	__lowercase = None			,	):







						'''simple docstring'''




						lowerCamelCase_							:		Optional[Any]							       =							self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
						    __lowercase			,	__lowercase			,	__lowercase			,	__lowercase			,	__lowercase )

						# Generate decoder inputs
						lowerCamelCase_							:		Dict							       =							seq_length if not self.use_past else 1
						lowerCamelCase_							:		List[str]							       =							self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
						    __lowercase			,	__lowercase			,	__lowercase			,	__lowercase			,	__lowercase )
						lowerCamelCase_							:		Any							       =							{f"decoder_{name}": tensor for name, tensor in decoder_inputs.items()}
						lowerCamelCase_							:		str							       =							dict(**__lowercase			,	**__lowercase )

						if self.use_past:
							if not is_torch_available():
								raise ValueError('Cannot generate dummy past_keys inputs without PyTorch installed.' )
							else:
								import torch
							lowerCamelCase_       ,      lowerCamelCase_							:		int							       =							common_inputs['input_ids'].shape
							lowerCamelCase_							:		List[Any]							       =							common_inputs['decoder_input_ids'].shape[1]
							lowerCamelCase_       ,      lowerCamelCase_							:		int							       =							self.num_attention_heads
							lowerCamelCase_							:		Any							       =							(
							    batch,
							    num_encoder_attention_heads,
							    encoder_seq_length,
							    self._config.hidden_size // num_encoder_attention_heads,
							)
							lowerCamelCase_							:		Tuple							       =							decoder_seq_length + 3
							lowerCamelCase_							:		Any							       =							(
							    batch,
							    num_decoder_attention_heads,
							    decoder_past_length,
							    self._config.hidden_size // num_decoder_attention_heads,
							)

							lowerCamelCase_							:		List[Any]							       =							torch.cat(
							    [common_inputs['decoder_attention_mask'], torch.ones(__lowercase			,	__lowercase )]			,	dim=1 )

							lowerCamelCase_							:		Tuple							       =							[]
							# If the number of encoder and decoder layers are present in the model configuration, both are considered
							lowerCamelCase_       ,      lowerCamelCase_							:		int							       =							self.num_layers
							lowerCamelCase_							:		Optional[int]							       =							min(__lowercase			,	__lowercase )
							lowerCamelCase_							:		int							       =							max(__lowercase			,	__lowercase ) - min_num_layers
							lowerCamelCase_							:		Union[str, Any]							       =							'encoder' if num_encoder_layers > num_decoder_layers else 'decoder'

							for _ in range(__lowercase ):
								common_inputs["past_key_values"].append(
								    (
								        torch.zeros(__lowercase ),
								        torch.zeros(__lowercase ),
								        torch.zeros(__lowercase ),
								        torch.zeros(__lowercase ),
								    ) )
							# TODO: test this.
							lowerCamelCase_							:		Optional[int]							       =							encoder_shape if remaining_side_name == 'encoder' else decoder_shape
							for _ in range(__lowercase			,	__lowercase ):
								common_inputs["past_key_values"].append((torch.zeros(__lowercase ), torch.zeros(__lowercase )) )
						return common_inputs





					_lowerCamelCase		  =			_generate_dummy_inputs_for_default_and_seqaseq_lm
