




from __future__ import annotations

import math



def      __lowerCAmelCase			(					UpperCamelCase      )     ->	bool:

  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(UpperCamelCase      ) + 1      )	,      6      ):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True


lowerCAmelCase_					    = [num for num in range(3, 10_00_01, 2) if not is_prime(num)]



def      __lowerCAmelCase			(					UpperCamelCase      )     ->	list[int]:
  if not isinstance(UpperCamelCase	,      UpperCamelCase      ):
    raise ValueError('''n must be an integer'''      )
  if n <= 0:
    raise ValueError('''n must be >= 0'''      )

  lowerCAmelCase__				:  Optional[int]		       =     []
  for num in range(len(UpperCamelCase      )      ):
    lowerCAmelCase__				:  Tuple		       =     0
    while 2 * i * i <= odd_composites[num]:
      lowerCAmelCase__				:  Tuple		       =     odd_composites[num] - 2 * i * i
      if is_prime(UpperCamelCase      ):
        break
      i += 1
    else:
      list_nums.append(odd_composites[num]      )
      if len(UpperCamelCase      ) == n:
        return list_nums

  return []



def      __lowerCAmelCase			(					)     ->	int:
  return compute_nums(1      )[0]


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







from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCAmelCase_					    = {
    """configuration_longformer""": [
        """LONGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """LongformerConfig""",
        """LongformerOnnxConfig""",
    ],
    """tokenization_longformer""": ["""LongformerTokenizer"""],
}

try:
     if not is_tokenizers_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowerCAmelCase_					    = ["""LongformerTokenizerFast"""]

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowerCAmelCase_					    = [
         """LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST""",
         """LongformerForMaskedLM""",
         """LongformerForMultipleChoice""",
         """LongformerForQuestionAnswering""",
         """LongformerForSequenceClassification""",
         """LongformerForTokenClassification""",
         """LongformerModel""",
         """LongformerPreTrainedModel""",
         """LongformerSelfAttention""",
     ]

try:
     if not is_tf_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowerCAmelCase_					    = [
         """TF_LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST""",
         """TFLongformerForMaskedLM""",
         """TFLongformerForMultipleChoice""",
         """TFLongformerForQuestionAnswering""",
         """TFLongformerForSequenceClassification""",
         """TFLongformerForTokenClassification""",
         """TFLongformerModel""",
         """TFLongformerPreTrainedModel""",
         """TFLongformerSelfAttention""",
     ]


if TYPE_CHECKING:
     from .configuration_longformer import (
         LONGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
         LongformerConfig,
         LongformerOnnxConfig,
     )
     from .tokenization_longformer import LongformerTokenizer

     try:
          if not is_tokenizers_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_longformer_fast import LongformerTokenizerFast

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_longformer import (
              LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
              LongformerForMaskedLM,
              LongformerForMultipleChoice,
              LongformerForQuestionAnswering,
              LongformerForSequenceClassification,
              LongformerForTokenClassification,
              LongformerModel,
              LongformerPreTrainedModel,
              LongformerSelfAttention,
          )

     try:
          if not is_tf_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_tf_longformer import (
              TF_LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
              TFLongformerForMaskedLM,
              TFLongformerForMultipleChoice,
              TFLongformerForQuestionAnswering,
              TFLongformerForSequenceClassification,
              TFLongformerForTokenClassification,
              TFLongformerModel,
              TFLongformerPreTrainedModel,
              TFLongformerSelfAttention,
          )

else:
     import sys

     lowerCAmelCase_					    = _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

