


'''simple docstring'''


import math
from decimal import Decimal, getcontext






def 			__lowerCAmelCase			(__lowerCAmelCase = 4_000_000 ):

		try:
				_UpperCAmelCase		:							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." )
		_UpperCAmelCase		:							Tuple             =   100
		_UpperCAmelCase		:							List[Any]             =   (Decimal(5 ) ** Decimal(0.5 ) + 1) / Decimal(2 )

		_UpperCAmelCase		:							Tuple             =   (math.floor(math.log(n * (phi + 2)   ,			__lowerCAmelCase ) - 1 ) // 3) * 3 + 2
		_UpperCAmelCase		:							Tuple             =   Decimal(round(phi ** Decimal(index + 1 ) ) ) / (phi + 2)
		_UpperCAmelCase		:							List[str]             =   num // 2
		return int(__lowerCAmelCase )


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







'''simple docstring'''


import torch
from torch import autograd






class 						lowerCAmelCase__      (      autograd.Function						):




			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  Optional[int]						,	lowerCamelCase__	:  torch.tensor						,	lowerCamelCase__	:  float						,	lowerCamelCase__	:  bool			) ->Optional[Any]:



					'''simple docstring'''







					_UpperCAmelCase		:							Optional[int]             =   inputs.numel()
					_UpperCAmelCase		:							Any             =   int(0.0_0_5 * nb_elems			) + 1
					if sigmoid:
							_UpperCAmelCase		:							List[str]             =   (torch.sigmoid(lowerCamelCase__			) > threshold).type(inputs.type()			)
					else:
							_UpperCAmelCase		:							List[Any]             =   (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
							_UpperCAmelCase		:							str             =   inputs.flatten().kthvalue(max(nb_elems - nb_min						,	1			)			).values
							_UpperCAmelCase		:							str             =   (inputs > k_threshold).type(inputs.type()			)
					return mask






			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  List[Any]						,	lowerCamelCase__	:  Optional[int]			) ->Dict:



					'''simple docstring'''







					return gradOutput, None, None






class 						lowerCAmelCase__      (      autograd.Function						):




			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  Optional[int]						,	lowerCamelCase__	:  torch.tensor						,	lowerCamelCase__	:  float			) ->List[str]:



					'''simple docstring'''







					_UpperCAmelCase		:							Optional[int]             =   inputs.clone()
					_UpperCAmelCase       ,     _UpperCAmelCase		:							Tuple             =   inputs.flatten().sort(descending=lowerCamelCase__			)
					_UpperCAmelCase		:							Optional[int]             =   int(threshold * inputs.numel()			)

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






			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  Optional[int]						,	lowerCamelCase__	:  Any			) ->Union[str, Any]:



					'''simple docstring'''







					return gradOutput, None






class 						lowerCAmelCase__      (      UpperCAmelCase__						):




			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  torch.tensor						,	lowerCamelCase__	:  float			) ->Tuple:



					'''simple docstring'''







					_UpperCAmelCase		:							List[Any]             =   inputs.clone()
					_UpperCAmelCase       ,     _UpperCAmelCase		:							Optional[Any]             =   inputs.abs().flatten().sort(descending=lowerCamelCase__			)
					_UpperCAmelCase		:							int             =   int(threshold * inputs.numel()			)

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



