
'''simple docstring'''







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


_lowercase				:						List[str]												= logging.get_logger(__name__)

_lowercase				:						Any												= {
    "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 				lowerCAmelCase__     (						lowerCamelCase_  ):
					lowerCAmelCase_       =  '''m2m_100'''
					lowerCAmelCase_       =  ['''past_key_values''']
					lowerCAmelCase_       =  {'''num_attention_heads''': '''encoder_attention_heads''', '''hidden_size''': '''d_model'''}






					def __init__(     self       ,							__SCREAMING_SNAKE_CASE=12_81_12       ,							__SCREAMING_SNAKE_CASE=10_24       ,							__SCREAMING_SNAKE_CASE=12       ,							__SCREAMING_SNAKE_CASE=40_96       ,							__SCREAMING_SNAKE_CASE=16       ,							__SCREAMING_SNAKE_CASE=12       ,							__SCREAMING_SNAKE_CASE=40_96       ,							__SCREAMING_SNAKE_CASE=16       ,							__SCREAMING_SNAKE_CASE=0.05       ,							__SCREAMING_SNAKE_CASE=0.05       ,							__SCREAMING_SNAKE_CASE=True       ,							__SCREAMING_SNAKE_CASE=True       ,							__SCREAMING_SNAKE_CASE="relu"       ,							__SCREAMING_SNAKE_CASE=10_24       ,							__SCREAMING_SNAKE_CASE=0.1       ,							__SCREAMING_SNAKE_CASE=0.1       ,							__SCREAMING_SNAKE_CASE=0.0       ,							__SCREAMING_SNAKE_CASE=0.02       ,							__SCREAMING_SNAKE_CASE=2       ,							__SCREAMING_SNAKE_CASE=True       ,							__SCREAMING_SNAKE_CASE=1       ,							__SCREAMING_SNAKE_CASE=0       ,							__SCREAMING_SNAKE_CASE=2       ,							**__SCREAMING_SNAKE_CASE       ,							):


											"""simple docstring"""





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

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







class 				lowerCAmelCase__     (						lowerCamelCase_  ):






					@property
					def 			_snake_case					(     self	):


											"""simple docstring"""





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

											if self.use_past:
																	lowercase_			:  Optional[Any]									= {0: '''batch'''}
																	lowercase_			:  List[Any]									= {0: '''batch''', 1: '''past_decoder_sequence + sequence'''}
											else:
																	lowercase_			:  Any									= {0: '''batch''', 1: '''decoder_sequence'''}
																	lowercase_			:  Tuple									= {0: '''batch''', 1: '''decoder_sequence'''}

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






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE = -1       ,							__SCREAMING_SNAKE_CASE = -1       ,							__SCREAMING_SNAKE_CASE = False       ,							__SCREAMING_SNAKE_CASE = None       ,							):


											"""simple docstring"""





											lowercase_			:  List[Any]									= compute_effective_axis_dimension(
											    __SCREAMING_SNAKE_CASE       ,							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
											lowercase_			:  int									= tokenizer.num_special_tokens_to_add(__SCREAMING_SNAKE_CASE	)
											lowercase_			:  Tuple									= compute_effective_axis_dimension(
											    __SCREAMING_SNAKE_CASE       ,							fixed_dimension=OnnxConfig.default_fixed_sequence       ,							num_token_to_add=__SCREAMING_SNAKE_CASE	)

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






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE = -1       ,							__SCREAMING_SNAKE_CASE = -1       ,							__SCREAMING_SNAKE_CASE = False       ,							__SCREAMING_SNAKE_CASE = None       ,							):


											"""simple docstring"""





											lowercase_			:  str									= self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
											    __SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	)

											# Generate decoder inputs
											lowercase_			:  Dict									= seq_length if not self.use_past else 1
											lowercase_			:  Optional[Any]									= self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
											    __SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	)
											lowercase_			:  str									= {F'''decoder_{name}''': tensor for name, tensor in decoder_inputs.items()}
											lowercase_			:  Optional[int]									= dict(**__SCREAMING_SNAKE_CASE       ,							**__SCREAMING_SNAKE_CASE	)

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

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

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

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




					lowerCAmelCase_       =  _generate_dummy_inputs_for_default_and_seqaseq_lm





'''simple docstring'''







from itertools import combinations, product
def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				int   ,   __SCREAMING_SNAKE_CASE      :				int   ,   __SCREAMING_SNAKE_CASE      :				int   ,   __SCREAMING_SNAKE_CASE      :				int							):



						"""simple docstring"""





						if xa == ya == 0 or xa == ya == 0:
												return False
						lowercase_			:  Optional[Any]									= xa * xa + ya * ya
						lowercase_			:  List[str]									= xa * xa + ya * ya
						lowercase_			:  Any									= (xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
						return (
						    a_square + b_square == c_square
						    or a_square + c_square == b_square
						    or b_square + c_square == a_square
						)
def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				int = 50							):



						"""simple docstring"""





						return sum(
						    1
						    for pta, pta in combinations(product(range(limit + 1							)   ,   repeat=2							)   ,   2							)
						    if is_right(*__SCREAMING_SNAKE_CASE   ,   *__SCREAMING_SNAKE_CASE							)							)


if __name__ == "__main__":
							print(f"""{solution() = }""")



