



"""simple docstring"""







from itertools import product

def 							UpperCamelCase_       (       lowerCAmelCase__ :							int = 15		)		->  int:

  """simple docstring"""




  lowerCAmelCase_  :							float								=					0.0
  lowerCAmelCase_  :							float
  lowerCAmelCase_  :							int
  lowerCAmelCase_  :							int
  lowerCAmelCase_  :							int
  lowerCAmelCase_  :							int
  lowerCAmelCase_  :							tuple[int, ...]

  for series in product(range(2		)       ,  repeat=lowerCAmelCase__		):
    lowerCAmelCase_  :							List[str]								=					series.count(1		)
    lowerCAmelCase_  :							Dict								=					num_turns - num_blue
    if num_red >= num_blue:
      continue
    lowerCAmelCase_  :							Optional[int]								=					1.0
    for ind, col in enumerate(lowerCAmelCase__       ,  2		):
      if col == 0:
        prob *= (ind - 1) / ind
      else:
        prob *= 1 / ind

    total_prob += prob

  return int(1 / total_prob		)


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










"""simple docstring"""







import inspect

from diffusers.utils import is_flax_available
from diffusers.utils.testing_utils import require_flax


if is_flax_available():
     import jax







@require_flax
class  UpperCamelCase__  :




      """simple docstring"""




      def 	SCREAMING_SNAKE_CASE__					( self							: Optional[int]			):
        lowerCAmelCase_		,lowerCAmelCase_  :							Any								=					self.prepare_init_args_and_inputs_for_common()

        lowerCAmelCase_  :							List[str]								=					self.model_class(**SCREAMING_SNAKE_CASE_			)
        lowerCAmelCase_  :							Any								=					model.init(inputs_dict['prng_key']       ,     inputs_dict['sample']			)
        jax.lax.stop_gradient(SCREAMING_SNAKE_CASE_			)

        lowerCAmelCase_  :							Tuple								=					model.apply(SCREAMING_SNAKE_CASE_       ,     inputs_dict['sample']			)

        if isinstance(SCREAMING_SNAKE_CASE_       ,     SCREAMING_SNAKE_CASE_			):
          lowerCAmelCase_  :							str								=					output.sample

        self.assertIsNotNone(SCREAMING_SNAKE_CASE_			)
        lowerCAmelCase_  :							Any								=					inputs_dict['sample'].shape
        self.assertEqual(output.shape       ,     SCREAMING_SNAKE_CASE_       ,     'Input and output shapes do not match'			)



      def 	SCREAMING_SNAKE_CASE__					( self							: List[str]			):
        lowerCAmelCase_		,lowerCAmelCase_  :							Union[str, Any]								=					self.prepare_init_args_and_inputs_for_common()

        lowerCAmelCase_  :							Tuple								=					1_6
        lowerCAmelCase_  :							Dict								=					(1_6, 3_2)

        lowerCAmelCase_  :							Any								=					self.model_class(**SCREAMING_SNAKE_CASE_			)
        lowerCAmelCase_  :							Optional[Any]								=					model.init(inputs_dict['prng_key']       ,     inputs_dict['sample']			)
        jax.lax.stop_gradient(SCREAMING_SNAKE_CASE_			)

        lowerCAmelCase_  :							Optional[Any]								=					model.apply(SCREAMING_SNAKE_CASE_       ,     inputs_dict['sample']			)

        if isinstance(SCREAMING_SNAKE_CASE_       ,     SCREAMING_SNAKE_CASE_			):
          lowerCAmelCase_  :							Dict								=					output.sample

        self.assertIsNotNone(SCREAMING_SNAKE_CASE_			)
        lowerCAmelCase_  :							Optional[Any]								=					inputs_dict['sample'].shape
        self.assertEqual(output.shape       ,     SCREAMING_SNAKE_CASE_       ,     'Input and output shapes do not match'			)





      def 	SCREAMING_SNAKE_CASE__					( self							: List[Any]			):
        lowerCAmelCase_  :							List[str]								=					'kwargs' in inspect.signature(self.model_class.__init__			).parameters
        lowerCAmelCase_  :							Optional[Any]								=					len(self.model_class._deprecated_kwargs			) > 0

        if has_kwarg_in_model_class and not has_deprecated_kwarg:
          raise ValueError(
              F"{self.model_class} has `**kwargs` in its __init__ method but has not defined any deprecated kwargs"
              ' under the `_deprecated_kwargs` class attribute. Make sure to either remove `**kwargs` if there are'
              ' no deprecated arguments or add the deprecated argument with `_deprecated_kwargs ='
              ' [<deprecated_argument>]`'			)

        if not has_kwarg_in_model_class and has_deprecated_kwarg:
          raise ValueError(
              F"{self.model_class} doesn't have `**kwargs` in its __init__ method but has defined deprecated kwargs"
              ' under the `_deprecated_kwargs` class attribute. Make sure to either add the `**kwargs` argument to'
              F" {self.model_class}.__init__ if there are deprecated arguments or remove the deprecated argument"
              ' from `_deprecated_kwargs = [<deprecated_argument>]`'			)





