

"""simple docstring"""





import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import (
    TaBlock,
    TaConfig,
    TaLayerNorm,
)

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin

class      __a (   _a,     _a,     _a     ):

			"""simple docstring"""

			@register_to_config
			def __init__(				self  :       str    ,	lowercase_  :       int    ,	lowercase_  :       int    ,	lowercase_  :       int    ,	lowercase_  :       float    ,	lowercase_  :       int    ,	lowercase_  :       int    ,	lowercase_  :       int    ,	lowercase_  :       int    ,	lowercase_  :       str    ,	lowercase_  :       bool = False    ,	):
								super().__init__()

								UpperCamelCase__		:     Tuple								=nn.Linear(lowercase_    ,	lowercase_    ,	bias=lowercase_    )

								UpperCamelCase__		:     Optional[Any]								=nn.Embedding(lowercase_    ,	lowercase_    )
								UpperCamelCase__		:     Optional[Any]								=False

								UpperCamelCase__		:     Tuple								=nn.Dropout(p=lowercase_    )

								UpperCamelCase__		:     Tuple								=TaConfig(
								    d_model=lowercase_    ,	num_heads=lowercase_    ,	d_kv=lowercase_    ,	d_ff=lowercase_    ,	feed_forward_proj=lowercase_    ,	dropout_rate=lowercase_    ,	is_decoder=lowercase_    ,	is_encoder_decoder=lowercase_    ,	)
								UpperCamelCase__		:     List[str]								=nn.ModuleList()
								for lyr_num in range(lowercase_    ):
													UpperCamelCase__		:     Any								=TaBlock(lowercase_    )
													self.encoders.append(lowercase_    )

								UpperCamelCase__		:     int								=TaLayerNorm(lowercase_    )
								UpperCamelCase__		:     Tuple								=nn.Dropout(p=lowercase_    )






			def  _lowerCAmelCase      (				self  :       List[Any]    ,	lowercase_  :       Any    ,	lowercase_  :       Dict    ):
								UpperCamelCase__		:     Any								=self.input_proj(lowercase_    )

								# terminal relative positional encodings
								UpperCamelCase__		:     Tuple								=encoder_inputs.shape[1]
								UpperCamelCase__		:     str								=torch.arange(lowercase_    ,	device=encoder_inputs.device    )

								UpperCamelCase__		:     Any								=encoder_inputs_mask.sum(-1    )
								UpperCamelCase__		:     Any								=torch.roll(input_positions.unsqueeze(0    )    ,	tuple(seq_lens.tolist()    )    ,	dims=0    )
								x += self.position_encoding(lowercase_    )

								UpperCamelCase__		:     List[str]								=self.dropout_pre(lowercase_    )

								# inverted the attention mask
								UpperCamelCase__		:     List[Any]								=encoder_inputs.size()
								UpperCamelCase__		:     List[Any]								=self.get_extended_attention_mask(lowercase_    ,	lowercase_    )

								for lyr in self.encoders:
													UpperCamelCase__		:     int								=lyr(lowercase_    ,	lowercase_    )[0]
								UpperCamelCase__		:     Union[str, Any]								=self.layer_norm(lowercase_    )

								return self.dropout_post(lowercase_    ), encoder_inputs_mask



import math
def 					__lowercase						(    lowerCamelCase__       )					->bool:

  '''simple docstring'''




  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5			,					int(math.sqrt(lowerCamelCase__       ) + 1       )			,					6       ):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True
def 					__lowercase						(    lowerCamelCase__ = 2_00_00_00       )					->int:

  '''simple docstring'''




  return sum(num for num in range(3			,					lowerCamelCase__			,					2       ) if is_prime(lowerCamelCase__       )       ) + 2 if n > 2 else 0


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

