
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


A		:   Any         =    logging.get_logger(__name__)

A		:   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       a_   ( _a						):
			a  : Dict				      =       '''m2m_100'''
			a  : Any				      =       ['''past_key_values''']
			a  : int				      =       {'''num_attention_heads''': '''encoder_attention_heads''', '''hidden_size''': '''d_model'''}






			def __init__(			self							, __UpperCamelCase=128_112							, __UpperCamelCase=1_024							, __UpperCamelCase=12							, __UpperCamelCase=4_096							, __UpperCamelCase=16							, __UpperCamelCase=12							, __UpperCamelCase=4_096							, __UpperCamelCase=16							, __UpperCamelCase=0.05							, __UpperCamelCase=0.05							, __UpperCamelCase=True							, __UpperCamelCase=True							, __UpperCamelCase="relu"							, __UpperCamelCase=1_024							, __UpperCamelCase=0.1							, __UpperCamelCase=0.1							, __UpperCamelCase=0.0							, __UpperCamelCase=0.02							, __UpperCamelCase=2							, __UpperCamelCase=True							, __UpperCamelCase=1							, __UpperCamelCase=0							, __UpperCamelCase=2							, **__UpperCamelCase							, ):
									_lowercase									=				vocab_size
									_lowercase									=				max_position_embeddings
									_lowercase									=				d_model
									_lowercase									=				encoder_ffn_dim
									_lowercase									=				encoder_layers
									_lowercase									=				encoder_attention_heads
									_lowercase									=				decoder_ffn_dim
									_lowercase									=				decoder_layers
									_lowercase									=				decoder_attention_heads
									_lowercase									=				dropout
									_lowercase									=				attention_dropout
									_lowercase									=				activation_dropout
									_lowercase									=				activation_function
									_lowercase									=				init_std
									_lowercase									=				encoder_layerdrop
									_lowercase									=				decoder_layerdrop
									_lowercase									=				use_cache
									_lowercase									=				encoder_layers
									_lowercase									=				scale_embedding  # scale factor will be sqrt(d_model) if True

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







class       a_   ( _a						):






			@property
			def       UpperCamelCase_							(			self     ):
									_lowercase									=				OrderedDict(
									    [
									        ("""input_ids""", {0: """batch""", 1: """encoder_sequence"""}),
									        ("""attention_mask""", {0: """batch""", 1: """encoder_sequence"""}),
									    ]     )

									if self.use_past:
															_lowercase									=				{0: """batch"""}
															_lowercase									=				{0: """batch""", 1: """past_decoder_sequence + sequence"""}
									else:
															_lowercase									=				{0: """batch""", 1: """decoder_sequence"""}
															_lowercase									=				{0: """batch""", 1: """decoder_sequence"""}

									if self.use_past:
															self.fill_with_past_key_values_(__UpperCamelCase							, direction="""inputs"""     )
									return common_inputs






			def       UpperCamelCase_							(			self							, __UpperCamelCase							, __UpperCamelCase = -1							, __UpperCamelCase = -1							, __UpperCamelCase = False							, __UpperCamelCase = None							, ):
									# Copied from OnnxConfig.generate_dummy_inputs
									# Did not use super(OnnxConfigWithPast, self).generate_dummy_inputs for code clarity.
									# If dynamic axis (-1) we forward with a fixed dimension of 2 samples to avoid optimizations made by ONNX
									_lowercase									=				compute_effective_axis_dimension(
									    __UpperCamelCase							, 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									=				tokenizer.num_special_tokens_to_add(__UpperCamelCase     )
									_lowercase									=				compute_effective_axis_dimension(
									    __UpperCamelCase							, fixed_dimension=OnnxConfig.default_fixed_sequence							, num_token_to_add=__UpperCamelCase     )

									# Generate dummy inputs according to compute batch and sequence
									_lowercase									=				[""" """.join([tokenizer.unk_token]     ) * seq_length] * batch_size
									_lowercase									=				dict(tokenizer(__UpperCamelCase							, return_tensors=__UpperCamelCase     )     )
									return common_inputs






			def       UpperCamelCase_							(			self							, __UpperCamelCase							, __UpperCamelCase = -1							, __UpperCamelCase = -1							, __UpperCamelCase = False							, __UpperCamelCase = None							, ):
									_lowercase									=				self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
									    __UpperCamelCase							, __UpperCamelCase							, __UpperCamelCase							, __UpperCamelCase							, __UpperCamelCase     )

									# Generate decoder inputs
									_lowercase									=				seq_length if not self.use_past else 1
									_lowercase									=				self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
									    __UpperCamelCase							, __UpperCamelCase							, __UpperCamelCase							, __UpperCamelCase							, __UpperCamelCase     )
									_lowercase									=				{f"""decoder_{name}""": tensor for name, tensor in decoder_inputs.items()}
									_lowercase									=				dict(**__UpperCamelCase							, **__UpperCamelCase     )

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

															_lowercase									=				torch.cat(
															    [common_inputs["""decoder_attention_mask"""], torch.ones(__UpperCamelCase							, __UpperCamelCase     )]							, dim=1     )

															_lowercase									=				[]
															# If the number of encoder and decoder layers are present in the model configuration, both are considered
															_lowercase					,	_lowercase									=				self.num_layers
															_lowercase									=				min(__UpperCamelCase							, __UpperCamelCase     )
															_lowercase									=				max(__UpperCamelCase							, __UpperCamelCase     ) - min_num_layers
															_lowercase									=				"""encoder""" if num_encoder_layers > num_decoder_layers else """decoder"""

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

			a  : int				      =       _generate_dummy_inputs_for_default_and_seqaseq_lm

def   UpperCamelCase__     (    SCREAMING_SNAKE_CASE_  :  int					)     ->    int:
						return n * (2 * n - 1)




def   UpperCamelCase__     (    SCREAMING_SNAKE_CASE_  :  int					)     ->    bool:
						_lowercase									=				(1 + 24 * n) ** 0.5
						return ((1 + root) / 6) % 1 == 0




def   UpperCamelCase__     (    SCREAMING_SNAKE_CASE_  :  int = 1_44					)     ->    int:
						_lowercase									=				start
						_lowercase									=				hexagonal_num(SCREAMING_SNAKE_CASE_					)
						while not is_pentagonal(SCREAMING_SNAKE_CASE_					):
												n += 1
												_lowercase									=				hexagonal_num(SCREAMING_SNAKE_CASE_					)
						return num


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