





'''simple docstring'''




from math import ceil






def        _lowerCAmelCase			(  __snake_case  : Optional[int] ,							__snake_case  : Tuple			)     ->     Tuple:
     __A						: str      =       list(range(0 ,							__snake_case			)			)

     __A						: int      =       [item for sublist in list(device_map.values()			) for item in sublist]

     # Duplicate check
     __A						: Tuple      =       []
     for i in device_map_blocks:
          if device_map_blocks.count(__snake_case			) > 1 and i not in duplicate_blocks:
               duplicate_blocks.append(__snake_case			)
    # Missing blocks
     __A						: str      =       [i for i in blocks if i not in device_map_blocks]
     __A						: Dict      =       [i for i in device_map_blocks if i not in blocks]

     if len(__snake_case			) != 0:
          raise ValueError(
              'Duplicate attention blocks specified in device_map. Attention blocks must be specified to one device.'
              ' These attention blocks were specified more than once: ' + str(__snake_case			)			)
     if len(__snake_case			) != 0:
          raise ValueError(
              'There are attention blocks for this model that are not specified in the device_map. Add these attention '
              'blocks to a device on the device_map: ' + str(__snake_case			)			)
     if len(__snake_case			) != 0:
          raise ValueError(
              'The device_map contains more attention blocks than this model has. Remove these from the device_map:'
              + str(__snake_case			)			)







def        _lowerCAmelCase			(  __snake_case  : Dict ,							__snake_case  : Tuple			)     ->     Optional[Any]:
     __A						: Dict      =       list(range(__snake_case			)			)
     __A						: int      =       int(ceil(n_layers / len(__snake_case			)			)			)
     __A						: Any      =       [layers[i : i + n_blocks] for i in range(0 ,							__snake_case ,							__snake_case			)]

     return dict(zip(__snake_case ,							__snake_case			)			)






'''simple docstring'''




import math






def        _lowerCAmelCase			(  __snake_case  : int			)     ->     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(__snake_case			) + 1			) ,							6			):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True






def        _lowerCAmelCase			(  __snake_case  : float = 0.1			)     ->     int:
     __A						: Tuple      =       3
     __A						: Optional[int]      =       3

     while primes / (2 * j - 1) >= ratio:
          for i in range(j * j + j + 1 ,							(j + 2) * (j + 2) ,							j + 1			):
               primes += is_prime(__snake_case			)
          j += 2
     return j


if __name__ == "__main__":
  import doctest

  doctest.testmod()