



def 						UpperCAmelCase (    ):

			for a in range(300     ):
						for b in range(a + 1			,     400     ):
									for c in range(b + 1			,     500     ):
												if (a + b + c) == 1000 and (a**2) + (b**2) == (c**2):
															return a * b * c

			return -1




def 						UpperCAmelCase (    ):

			for a in range(300     ):
						for b in range(400     ):
									A				:       List[str]														=    1000 - a - b
									if a < b < c and (a**2) + (b**2) == (c**2):
												return a * b * c

			return -1




def 						UpperCAmelCase (    ):
			import timeit

			print(
			    timeit.timeit("solution()"			,     setup="from __main__ import solution"			,     number=1000     )     )
			print(
			    timeit.timeit(
			        "solution_fast()"			,     setup="from __main__ import solution_fast"			,     number=1000     )     )


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



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

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


UpperCAmelCase     =       logging.get_logger(__name__)

UpperCAmelCase     =       {
    """facebook/blenderbot-3B""": """https://huggingface.co/facebook/blenderbot-3B/resolve/main/config.json""",
    # See all Blenderbot models at https://huggingface.co/models?filter=blenderbot
}







class lowerCAmelCase_		(					lowerCamelCase__			):

 '''simple docstring'''

 __snake_case				=    "blenderbot"
 __snake_case				=    ["past_key_values"]
 __snake_case				=    {"num_attention_heads": "encoder_attention_heads", "hidden_size": "d_model"}



 def __init__(      self						, _UpperCAmelCase=80_08						, _UpperCAmelCase=1_28						, _UpperCAmelCase=2						, _UpperCAmelCase=1_02_40						, _UpperCAmelCase=32						, _UpperCAmelCase=24						, _UpperCAmelCase=1_02_40						, _UpperCAmelCase=32						, _UpperCAmelCase=0.0						, _UpperCAmelCase=0.0						, _UpperCAmelCase=True						, _UpperCAmelCase=True						, _UpperCAmelCase="gelu"						, _UpperCAmelCase=25_60						, _UpperCAmelCase=0.1						, _UpperCAmelCase=0.0						, _UpperCAmelCase=0.0						, _UpperCAmelCase=0.02						, _UpperCAmelCase=1						, _UpperCAmelCase=False						, _UpperCAmelCase=0						, _UpperCAmelCase=1						, _UpperCAmelCase=2						, _UpperCAmelCase=3						, _UpperCAmelCase=2						, **_UpperCAmelCase						, ):
       snake_case_			= vocab_size
       snake_case_			= max_position_embeddings
       snake_case_			= d_model
       snake_case_			= encoder_ffn_dim
       snake_case_			= encoder_layers
       snake_case_			= encoder_attention_heads
       snake_case_			= decoder_ffn_dim
       snake_case_			= decoder_layers
       snake_case_			= decoder_attention_heads
       snake_case_			= dropout
       snake_case_			= attention_dropout
       snake_case_			= activation_dropout
       snake_case_			= activation_function
       snake_case_			= init_std
       snake_case_			= encoder_layerdrop
       snake_case_			= decoder_layerdrop
       snake_case_			= use_cache
       snake_case_			= encoder_layers
       snake_case_			= 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						, encoder_no_repeat_ngram_size=_UpperCAmelCase						, forced_eos_token_id=_UpperCAmelCase						, **_UpperCAmelCase						, )







class lowerCAmelCase_		(					lowerCamelCase__			):

 '''simple docstring'''

 @property
 def 		UpperCamelCase__	(      self   ):
       if self.task in ["default", "seq2seq-lm"]:
             snake_case_			= OrderedDict(
                 [
                     ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
                     ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
                 ]   )
             if self.use_past:
                   snake_case_			= {0: '''batch'''}
                   snake_case_			= {0: '''batch''', 1: '''past_decoder_sequence + sequence'''}
             else:
                   snake_case_			= {0: '''batch''', 1: '''decoder_sequence'''}
                   snake_case_			= {0: '''batch''', 1: '''decoder_sequence'''}
             if self.use_past:
                   self.fill_with_past_key_values_(_UpperCAmelCase						, direction='''inputs'''   )
       elif self.task == "causal-lm":
             snake_case_			= OrderedDict(
                 [
                     ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
                     ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
                 ]   )
             if self.use_past:
                   snake_case_			,       snake_case_			= self.num_layers
                   for i in range(_UpperCAmelCase   ):
                         snake_case_			= {0: '''batch''', 2: '''past_sequence + sequence'''}
                         snake_case_			= {0: '''batch''', 2: '''past_sequence + sequence'''}
       else:
             snake_case_			= OrderedDict(
                 [
                     ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
                     ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
                     ('''decoder_input_ids''', {0: '''batch''', 1: '''decoder_sequence'''}),
                     ('''decoder_attention_mask''', {0: '''batch''', 1: '''decoder_sequence'''}),
                 ]   )

       return common_inputs



 @property
 # Copied from transformers.models.bart.configuration_bart.BartOnnxConfig.outputs
 def 		UpperCamelCase__	(      self   ):
       if self.task in ["default", "seq2seq-lm"]:
             snake_case_			= super().outputs
       else:
             snake_case_			= super(_UpperCAmelCase						, self   ).outputs
             if self.use_past:
                   snake_case_			,       snake_case_			= self.num_layers
                   for i in range(_UpperCAmelCase   ):
                         snake_case_			= {0: '''batch''', 2: '''past_sequence + sequence'''}
                         snake_case_			= {0: '''batch''', 2: '''past_sequence + sequence'''}
       return common_outputs



 def 		UpperCamelCase__	(      self						, _UpperCAmelCase						, _UpperCAmelCase = -1						, _UpperCAmelCase = -1						, _UpperCAmelCase = False						, _UpperCAmelCase = None						, ):
       snake_case_			= self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
           _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase   )
       # Generate decoder inputs
       snake_case_			= seq_length if not self.use_past else 1
       snake_case_			= self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
           _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase   )
       snake_case_			= {F'''decoder_{name}''': tensor for name, tensor in decoder_inputs.items()}
       snake_case_			= 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
             snake_case_			,       snake_case_			= common_inputs['''input_ids'''].shape
             snake_case_			= common_inputs['''decoder_input_ids'''].shape[1]
             snake_case_			,       snake_case_			= self.num_attention_heads
             snake_case_			= (
                 batch,
                 num_encoder_attention_heads,
                 encoder_seq_length,
                 self._config.hidden_size // num_encoder_attention_heads,
             )
             snake_case_			= decoder_seq_length
             snake_case_			= (
                 batch,
                 num_decoder_attention_heads,
                 decoder_past_length,
                 self._config.hidden_size // num_decoder_attention_heads,
             )
             snake_case_			= torch.cat(
                 [common_inputs['''decoder_attention_mask'''], torch.ones(_UpperCAmelCase						, _UpperCAmelCase   )]						, dim=1   )
             snake_case_			= []
             snake_case_			,       snake_case_			= self.num_layers

             for _ in range(_UpperCAmelCase   ):
                   common_inputs["past_key_values"].append(
                       (
                           torch.zeros(_UpperCAmelCase   ),
                           torch.zeros(_UpperCAmelCase   ),
                           torch.zeros(_UpperCAmelCase   ),
                           torch.zeros(_UpperCAmelCase   ),
                       )   )
       return common_inputs



 def 		UpperCamelCase__	(      self						, _UpperCAmelCase						, _UpperCAmelCase = -1						, _UpperCAmelCase = -1						, _UpperCAmelCase = False						, _UpperCAmelCase = None						, ):
       snake_case_			= self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
           _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase						, _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
             snake_case_			,       snake_case_			= common_inputs['''input_ids'''].shape
             snake_case_			= seqlen
             snake_case_			,       snake_case_			= self.num_layers
             snake_case_			,       snake_case_			= self.num_attention_heads
             snake_case_			= (
                 batch,
                 num_encoder_attention_heads,
                 past_key_values_length,
                 self._config.hidden_size // num_encoder_attention_heads,
             )
             snake_case_			= common_inputs['''attention_mask'''].dtype
             snake_case_			= torch.cat(
                 [common_inputs['''attention_mask'''], torch.ones(_UpperCAmelCase						, _UpperCAmelCase						, dtype=_UpperCAmelCase   )]						, dim=1   )
             snake_case_			= [
                 (torch.zeros(_UpperCAmelCase   ), torch.zeros(_UpperCAmelCase   )) for _ in range(_UpperCAmelCase   )
             ]
       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
       snake_case_			= 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
       snake_case_			= tokenizer.num_special_tokens_to_add(_UpperCAmelCase   )
       snake_case_			= 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
       snake_case_			= [''' '''.join([tokenizer.unk_token]   ) * seq_length] * batch_size
       snake_case_			= dict(tokenizer(_UpperCAmelCase						, return_tensors=_UpperCAmelCase   )   )
       return common_inputs



 def 		UpperCamelCase__	(      self						, _UpperCAmelCase						, _UpperCAmelCase = -1						, _UpperCAmelCase = -1						, _UpperCAmelCase = False						, _UpperCAmelCase = None						, ):
       if self.task in ["default", "seq2seq-lm"]:
             snake_case_			= self._generate_dummy_inputs_for_default_and_seqaseq_lm(
                 _UpperCAmelCase						, batch_size=_UpperCAmelCase						, seq_length=_UpperCAmelCase						, is_pair=_UpperCAmelCase						, framework=_UpperCAmelCase   )

       elif self.task == "causal-lm":
             snake_case_			= self._generate_dummy_inputs_for_causal_lm(
                 _UpperCAmelCase						, batch_size=_UpperCAmelCase						, seq_length=_UpperCAmelCase						, is_pair=_UpperCAmelCase						, framework=_UpperCAmelCase   )
       else:
             snake_case_			= self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
                 _UpperCAmelCase						, batch_size=_UpperCAmelCase						, seq_length=_UpperCAmelCase						, is_pair=_UpperCAmelCase						, framework=_UpperCAmelCase   )

       return common_inputs



 def 		UpperCamelCase__	(      self						, _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase   ):
       if self.task in ["default", "seq2seq-lm"]:
             snake_case_			= super()._flatten_past_key_values_(_UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase   )
       else:
             snake_case_			= super(_UpperCAmelCase						, self   )._flatten_past_key_values_(
                 _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase						, _UpperCAmelCase   )





 def 		UpperCamelCase__	(      self						, _UpperCAmelCase						, _UpperCAmelCase   ):
       if direction not in ["inputs", "outputs"]:
             raise ValueError(F'''direction must either be "inputs" or "outputs", but {direction} was given'''   )

       snake_case_			= '''past_key_values''' if direction == '''inputs''' else '''present'''
       snake_case_			,       snake_case_			= self.num_layers

       snake_case_			= '''past_encoder_sequence'''
       snake_case_			= '''past_decoder_sequence''' if direction == '''inputs''' else '''past_decoder_sequence + sequence'''

       for i in range(_UpperCAmelCase   ):
             snake_case_			= {0: '''batch''', 2: decoder_sequence}
             snake_case_			= {0: '''batch''', 2: decoder_sequence}
             snake_case_			= {0: '''batch''', 2: encoder_sequence}
             snake_case_			= {0: '''batch''', 2: encoder_sequence}