
import math




def 				a						(							snake_case__:					int					):


				'''simple docstring'''
				assert isinstance(snake_case__						,   snake_case__					) and (
				    number >= 0
				), "'number' must been an int and positive"

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

				lowercase_       =					range(3						,   int(math.sqrt(snake_case__					) + 1					)						,   2					)
				return not any(not number % i for i in odd_numbers					)




def 				a						(							snake_case__:					Any						,   snake_case__:					Optional[Any]=1						,   **snake_case__:					Any					):


				'''simple docstring'''
				lowercase_       =					factor * value
				lowercase_       =					value

				while not is_prime(snake_case__					):
								value += 1 if not ("desc" in kwargs and kwargs["desc"] is True) else -1

				if value == first_value_val:
								return next_prime(value + 1						,   **snake_case__					)
				return value









from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_flax_available, is_torch_available


a_   :int        =      {
    "configuration_longt5": ["LONGT5_PRETRAINED_CONFIG_ARCHIVE_MAP", "LongT5Config", "LongT5OnnxConfig"],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 a_   :List[str]        =      [
     "LONGT5_PRETRAINED_MODEL_ARCHIVE_LIST",
     "LongT5EncoderModel",
     "LongT5ForConditionalGeneration",
     "LongT5Model",
     "LongT5PreTrainedModel",
 ]

try:
 if not is_flax_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 a_   :int        =      [
     "FlaxLongT5ForConditionalGeneration",
     "FlaxLongT5Model",
     "FlaxLongT5PreTrainedModel",
 ]


if TYPE_CHECKING:
 from .configuration_longta import LONGT5_PRETRAINED_CONFIG_ARCHIVE_MAP, LongTaConfig, LongTaOnnxConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_longta import (
      LONGT5_PRETRAINED_MODEL_ARCHIVE_LIST,
      LongTaEncoderModel,
      LongTaForConditionalGeneration,
      LongTaModel,
      LongTaPreTrainedModel,
  )

 try:
  if not is_flax_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_flax_longta import (
      FlaxLongTaForConditionalGeneration,
      FlaxLongTaModel,
      FlaxLongTaPreTrainedModel,
  )


else:
 import sys

 a_   :Optional[int]        =      _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)






