'''simple docstring'''
import json
import os
from collections.abc import Mapping
from typing import Dict, List, Optional, Union

import numpy as np
import torch

from .imports import is_safetensors_available







def 				__UpperCamelCase (					__UpperCAmelCase  :					Optional[Any] ,   __UpperCAmelCase  :					List[Any] ,   __UpperCAmelCase  :					List[Any] ,   __UpperCAmelCase  :					Union[str, Any]=None			)							->	Union[str, Any]:
  lowercase				:							str									=   None
  # Check the string instead of the dtype to be compatible with versions of PyTorch that don't have bfloat16.
  if str(weight.dtype			) == "torch.bfloat16":
    # Need to reinterpret the underlined data as int16 since NumPy does not handle bfloat16s.
    lowercase				:							Optional[int]									=   weight.view(torch.intaa			)
    lowercase				:							Any									=   '''bfloat16'''
  lowercase				:							Union[str, Any]									=   weight.cpu().numpy()
  lowercase				:							Optional[Any]									=   os.path.join(__UpperCAmelCase ,   f"""{weight_name}.dat"""			)
  if index is not None:
    if dtype is None:
      lowercase				:							Any									=   str(array.dtype			)
    lowercase				:							List[str]									=   {'''dtype''': dtype, '''shape''': list(array.shape			)}
  if array.ndim == 0:
    lowercase				:							Union[str, Any]									=   array[None]
  lowercase				:							Union[str, Any]									=   np.memmap(__UpperCAmelCase ,   dtype=array.dtype ,   mode='''w+''' ,   shape=array.shape			)
  lowercase				:							Dict									=   array[:]
  file_array.flush()
  return index







def 				__UpperCamelCase (					__UpperCAmelCase  :					List[str] ,   __UpperCAmelCase  :					Any			)							->	Optional[int]:
  lowercase				:							Tuple									=   tuple(weight_info['''shape''']			)
  if shape == ():
    # NumPy memory-mapped arrays can't have 0 dims so it was saved as 1d tensor
    lowercase				:							Union[str, Any]									=   (1,)

  lowercase				:							Optional[int]									=   weight_info['''dtype''']
  if dtype == "bfloat16":
    # NumPy does not support bfloat16 so this was saved as a int16
    lowercase				:							List[str]									=   '''int16'''

  lowercase				:							Optional[Any]									=   np.memmap(__UpperCAmelCase ,   dtype=__UpperCAmelCase ,   shape=__UpperCAmelCase ,   mode='''r'''			)

  if len(weight_info['''shape''']			) == 0:
    lowercase				:							Tuple									=   weight[0]
  lowercase				:							str									=   torch.tensor(__UpperCAmelCase			)
  if weight_info["dtype"] == "bfloat16":
    lowercase				:							Union[str, Any]									=   weight.view(torch.bfloataa			)

  return weight







def 				__UpperCamelCase (					__UpperCAmelCase  :					Optional[int] ,   __UpperCAmelCase  :					List[str]			)							->	List[str]:
  if index is None or len(__UpperCAmelCase			) == 0:
    # Nothing to save
    return

  lowercase				:							Union[str, Any]									=   os.path.join(__UpperCAmelCase ,   '''index.json'''			)
  if os.path.isfile(__UpperCAmelCase			):
    with open(__UpperCAmelCase ,   '''r''' ,   encoding='''utf-8'''			) as f:
      lowercase				:							List[Any]									=   json.load(__UpperCAmelCase			)
  else:
    lowercase				:							Union[str, Any]									=   {}
  current_index.update(__UpperCAmelCase			)

  with open(__UpperCAmelCase ,   '''w''' ,   encoding='''utf-8'''			) as f:
    json.dump(__UpperCAmelCase ,   __UpperCAmelCase ,   indent=2			)







def 				__UpperCamelCase (					__UpperCAmelCase  :					Union[str, os.PathLike] ,   __UpperCAmelCase  :					Dict[str, torch.Tensor]			)							->	List[Any]:
  os.makedirs(__UpperCAmelCase ,   exist_ok=__UpperCAmelCase			)
  lowercase				:							Optional[int]									=   {}
  for name, parameter in state_dict.items():
    lowercase				:							Dict									=   offload_weight(__UpperCAmelCase ,   __UpperCAmelCase ,   __UpperCAmelCase ,   index=__UpperCAmelCase			)

  # Update index
  save_offload_index(__UpperCAmelCase ,   __UpperCAmelCase			)




class _lowerCAmelCase			(	snake_case					):







      def __init__(  self  ,    lowercase  ,    lowercase     ):
        lowercase				:							Tuple									=   dataset
        lowercase				:							Any									=   prefix







      def __getitem__(  self  ,    lowercase     ):
        return self.dataset[F"""{self.prefix}{key}"""]







      def __iter__(  self     ):
        return iter([key for key in self.dataset if key.startswith(self.prefix     )]     )







      def __len__(  self     ):
        return len(self.dataset     )





class _lowerCAmelCase			(	snake_case					):







      def __init__(  self  ,    lowercase = None  ,    lowercase = None  ,    lowercase = None  ,    lowercase=None  ,    ):
        if state_dict is None and save_folder is None:
          raise ValueError('''Need either a `state_dict` or a `save_folder` containing offloaded weights.'''     )

        lowercase				:							Optional[Any]									=   {} if state_dict is None else state_dict
        lowercase				:							List[Any]									=   save_folder
        if index is None and save_folder is not None:
          with open(os.path.join(lowercase  ,    '''index.json'''     )     ) as f:
            lowercase				:							Any									=   json.load(lowercase     )
        lowercase				:							Union[str, Any]									=   {} if index is None else index
        lowercase				:							Union[str, Any]									=   list(self.state_dict.keys()     )
        self.all_keys.extend([key for key in self.index if key not in self.all_keys]     )
        lowercase				:							Union[str, Any]									=   device







      def __getitem__(  self  ,    lowercase     ):
        # State dict gets priority
        if key in self.state_dict:
          return self.state_dict[key]
        lowercase				:							Tuple									=   self.index[key]
        if weight_info.get('''safetensors_file'''     ) is not None:
          if not is_safetensors_available():
            raise ImportError('''These offloaded weights require the use of safetensors: `pip install safetensors`.'''     )

          from safetensors import safe_open

          lowercase				:							str									=   '''cpu''' if self.device is None else self.device
          with safe_open(weight_info['''safetensors_file''']  ,    framework='''pt'''  ,    device=lowercase     ) as f:
            lowercase				:							List[Any]									=   f.get_tensor(weight_info.get('''weight_name'''  ,    lowercase     )     )

          if "dtype" in weight_info:
            return tensor.to(getattr(lowercase  ,    weight_info['''dtype''']     )     )
          else:
            return tensor

        lowercase				:							int									=   os.path.join(self.save_folder  ,    F"""{key}.dat"""     )
        return load_offloaded_weight(lowercase  ,    lowercase     )







      def __iter__(  self     ):
        return iter(self.all_keys     )







      def __len__(  self     ):
        return len(self.all_keys     )







def 				__UpperCamelCase (					__UpperCAmelCase  :					Dict[str, torch.Tensor] ,   __UpperCAmelCase  :					List[str]			)							->	int:
  lowercase				:							Union[str, Any]									=   {}
  for module_name in submodule_names:
    # We want to catch module_name parameter (module_name.xxx) or potentially module_name, but not any of the
    # submodules that could being like module_name (transformers.h.1 and transformers.h.10 for instance)
    result.update(
        {
            key: param
            for key, param in state_dict.items()
            if key == module_name or key.startswith(module_name + '''.'''			)
        }			)
  return result
'''simple docstring'''
import math







def 				__UpperCamelCase (					__UpperCAmelCase  :					str			)							->	Optional[int]:
  lowercase				:							Tuple									=   0
  if n % 2 == 0:
    count += 1
    while n % 2 == 0:
      lowercase				:							Optional[int]									=   int(n / 2			)
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

  lowercase				:							Dict									=   3

  while i <= int(math.sqrt(__UpperCAmelCase			)			):
    if n % i == 0:
      count += 1
      while n % i == 0:
        lowercase				:							Dict									=   int(n / i			)
    lowercase				:							List[Any]									=   i + 2

  # this condition checks the prime
  # number n is greater than 2

  if n > 2:
    count += 1
  return count


if __name__ == "__main__":
 _A		:      List[Any]						   =5_1_2_4_2_1_8_3
 print(f"""The number of distinct prime factors is/are {exact_prime_factor_count(n)}""")
 print(f"""The value of log(log(n)) is {math.log(math.log(n)):.4f}""")