





'''simple docstring'''






import math







def 				_a	(					_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 				_a	(					_lowerCamelCase = 6008_5147_5143   )   ->							int:



   """simple docstring"""


   try:
      __snake_case				:			List[Any]       			=    int(_lowerCamelCase   )
   except (TypeError, ValueError):
      raise TypeError("""Parameter n must be int or castable to int."""   )
   if n <= 0:
      raise ValueError("""Parameter n must be greater than or equal to one."""   )
   __snake_case				:			List[str]       			=    0
   if is_prime(_lowerCamelCase   ):
      return n
   while n % 2 == 0:
      n //= 2
   if is_prime(_lowerCamelCase   ):
      return n
   for i in range(3						,  int(math.sqrt(_lowerCamelCase   )   ) + 1						,  2   ):
      if n % i == 0:
         if is_prime(n // i   ):
            __snake_case				:			Optional[Any]       			=    n // i
            break
         elif is_prime(_lowerCamelCase   ):
            __snake_case				:			Tuple       			=    i
   return max_number


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









'''simple docstring'''






import torch
from torch import autograd




class    _A   (				autograd.Function		):

		@staticmethod
		def   lowercase__    (      __magic_name__				:      List[Any]     ,			__magic_name__				:      torch.tensor     ,			__magic_name__				:      float     ,			__magic_name__				:      bool )				->						Optional[int]:


					"""simple docstring"""

					__snake_case				:			List[Any]       			=    inputs.numel()
					__snake_case				:			List[Any]       			=    int(0.005 * nb_elems ) + 1
					if sigmoid:
								__snake_case				:			Dict       			=    (torch.sigmoid(__magic_name__ ) > threshold).type(inputs.type() )
					else:
								__snake_case				:			Tuple       			=    (inputs > threshold).type(inputs.type() )
					if mask.sum() < nb_min:
								# We limit the pruning so that at least 0.5% (half a percent) of the weights are remaining
								__snake_case				:			Tuple       			=    inputs.flatten().kthvalue(max(nb_elems - nb_min     ,			1 ) ).values
								__snake_case				:			Union[str, Any]       			=    (inputs > k_threshold).type(inputs.type() )
					return mask

		@staticmethod
		def   lowercase__    (      __magic_name__				:      int     ,			__magic_name__				:      Any )				->						Tuple:


					"""simple docstring"""

					return gradOutput, None, None





class    _A   (				autograd.Function		):

		@staticmethod
		def   lowercase__    (      __magic_name__				:      Tuple     ,			__magic_name__				:      torch.tensor     ,			__magic_name__				:      float )				->						int:


					"""simple docstring"""

					__snake_case				:			Tuple       			=    inputs.clone()
					__snake_case			,    __snake_case				:			Dict       			=    inputs.flatten().sort(descending=__magic_name__ )
					__snake_case				:			List[Any]       			=    int(threshold * inputs.numel() )

					# flat_out and mask access the same memory.
					__snake_case				:			Optional[Any]       			=    mask.flatten()
					__snake_case				:			List[str]       			=    0
					__snake_case				:			Any       			=    1
					return mask

		@staticmethod
		def   lowercase__    (      __magic_name__				:      List[str]     ,			__magic_name__				:      Any )				->						Optional[Any]:


					"""simple docstring"""

					return gradOutput, None





class    _A   (				__lowercase		):

		@staticmethod
		def   lowercase__    (      __magic_name__				:      torch.tensor     ,			__magic_name__				:      float )				->						List[str]:


					"""simple docstring"""

					__snake_case				:			List[str]       			=    inputs.clone()
					__snake_case			,    __snake_case				:			Tuple       			=    inputs.abs().flatten().sort(descending=__magic_name__ )
					__snake_case				:			Any       			=    int(threshold * inputs.numel() )

					# flat_out and mask access the same memory.
					__snake_case				:			Union[str, Any]       			=    mask.flatten()
					__snake_case				:			Tuple       			=    0
					__snake_case				:			int       			=    1
					return mask


