"""simple docstring"""







import itertools



def       A__    (	lowercase_     :	int = 1000000						)  ->							int:
   __lowerCamelCase    		=					[1]

   for i in itertools.count(len(lowercase_						)						):
      __lowerCamelCase    		=					0
      for j in itertools.count(1						):
         __lowerCamelCase    		=					-1 if j % 2 == 0 else +1
         __lowerCamelCase    		=					(j * j * 3 - j) // 2
         if index > i:
            break
         item += partitions[i - index] * sign
         item %= number
         index += j
         if index > i:
            break
         item += partitions[i - index] * sign
         item %= number

      if item == 0:
         return i
      partitions.append(lowercase_						)

   return 0


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     print(F"{solution() = }")









import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowerCamelCase   					=  logging.get_logger(__name__)

lowerCamelCase   					=  {}





class      snake_case_      (					_a				):


							"""simple docstring"""





							__UpperCAmelCase      ="""fsmt_decoder"""




							def __init__(			self       ,    _A=0       ,    _A=0				):
												super().__init__()
												__lowerCAmelCase       =				vocab_size
												__lowerCAmelCase       =				bos_token_id





class      snake_case_      (					_a				):


							"""simple docstring"""





							__UpperCAmelCase      ="""fsmt"""
							__UpperCAmelCase      ={"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}




							def __init__(			self       ,    _A=["en", "de"]       ,    _A=4_2_0_2_4       ,    _A=4_2_0_2_4       ,    _A="relu"       ,    _A=1_0_2_4       ,    _A=2_0_0       ,    _A=1_0_2_4       ,    _A=4_0_9_6       ,    _A=1_2       ,    _A=1_6       ,    _A=0.0       ,    _A=4_0_9_6       ,    _A=1_2       ,    _A=1_6       ,    _A=0.0       ,    _A=0.0       ,    _A=0.1       ,    _A=0.0       ,    _A=0.02       ,    _A=2       ,    _A=True       ,    _A=True       ,    _A=False       ,    _A=5       ,    _A=1.0       ,    _A=False       ,    _A=True       ,    _A=1       ,    _A=0       ,    _A=2       ,    _A=2       ,    **_A       ,    ):
												__lowerCAmelCase       =				langs
												__lowerCAmelCase       =				src_vocab_size
												__lowerCAmelCase       =				tgt_vocab_size
												__lowerCAmelCase       =				d_model  # encoder_embed_dim and decoder_embed_dim

												__lowerCAmelCase       =				encoder_ffn_dim
												__lowerCAmelCase       =				__lowerCAmelCase       =				encoder_layers
												__lowerCAmelCase       =				encoder_attention_heads
												__lowerCAmelCase       =				encoder_layerdrop
												__lowerCAmelCase       =				decoder_layerdrop
												__lowerCAmelCase       =				decoder_ffn_dim
												__lowerCAmelCase       =				decoder_layers
												__lowerCAmelCase       =				decoder_attention_heads
												__lowerCAmelCase       =				max_position_embeddings
												__lowerCAmelCase       =				init_std  # Normal(0, this parameter)
												__lowerCAmelCase       =				activation_function

												__lowerCAmelCase       =				DecoderConfig(vocab_size=_A       ,    bos_token_id=_A				)
												if "decoder" in common_kwargs:
																	del common_kwargs["decoder"]

												__lowerCAmelCase       =				scale_embedding  # scale factor will be sqrt(d_model) if True

												# 3 Types of Dropout
												__lowerCAmelCase       =				attention_dropout
												__lowerCAmelCase       =				activation_dropout
												__lowerCAmelCase       =				dropout

												__lowerCAmelCase       =				use_cache
												super().__init__(
												    pad_token_id=_A       ,    bos_token_id=_A       ,    eos_token_id=_A       ,    decoder_start_token_id=_A       ,    is_encoder_decoder=_A       ,    tie_word_embeddings=_A       ,    forced_eos_token_id=_A       ,    max_length=_A       ,    num_beams=_A       ,    length_penalty=_A       ,    early_stopping=_A       ,    **_A       ,    )




							def 							A__	(			self				):
												__lowerCAmelCase       =				copy.deepcopy(self.__dict__				)
												__lowerCAmelCase       =				self.decoder.to_dict()
												__lowerCAmelCase       =				self.__class__.model_type
												return output






