'''simple docstring'''





def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: Dict				,  __UpperCamelCase					: Union[str, Any]			)							->      List[Any]:







  """simple docstring"""





  SCREAMING_SNAKE_CASE__    							=   0
  SCREAMING_SNAKE_CASE__    							=   len(_SCREAMING_SNAKE_CASE			) - 1

  while left <= right:
    # avoid divided by 0 during interpolation
    if sorted_collection[left] == sorted_collection[right]:
      if sorted_collection[left] == item:
        return left
      else:
        return None

    SCREAMING_SNAKE_CASE__    							=   left + ((item - sorted_collection[left]) * (right - left)) // (
        sorted_collection[right] - sorted_collection[left]
    )

    # out of range check
    if point < 0 or point >= len(_SCREAMING_SNAKE_CASE			):
      return None

    SCREAMING_SNAKE_CASE__    							=   sorted_collection[point]
    if current_item == item:
      return point
    else:
      if point < left:
        SCREAMING_SNAKE_CASE__    							=   left
        SCREAMING_SNAKE_CASE__    							=   point
      elif point > right:
        SCREAMING_SNAKE_CASE__    							=   right
        SCREAMING_SNAKE_CASE__    							=   point
      else:
        if item < current_item:
          SCREAMING_SNAKE_CASE__    							=   point - 1
        else:
          SCREAMING_SNAKE_CASE__    							=   point + 1
  return None



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: List[str]				,  __UpperCamelCase					: Dict				,  __UpperCamelCase					: Dict				,  __UpperCamelCase					: int			)							->      Optional[int]:







  """simple docstring"""





  if sorted_collection[left] == sorted_collection[right]:
    if sorted_collection[left] == item:
      return left
    else:
      return None

  SCREAMING_SNAKE_CASE__    							=   left + ((item - sorted_collection[left]) * (right - left)) // (
      sorted_collection[right] - sorted_collection[left]
  )

  # out of range check
  if point < 0 or point >= len(_SCREAMING_SNAKE_CASE			):
    return None

  if sorted_collection[point] == item:
    return point
  elif point < left:
    return interpolation_search_by_recursion(_SCREAMING_SNAKE_CASE				,  _SCREAMING_SNAKE_CASE				,  _SCREAMING_SNAKE_CASE				,  _SCREAMING_SNAKE_CASE			)
  elif point > right:
    return interpolation_search_by_recursion(_SCREAMING_SNAKE_CASE				,  _SCREAMING_SNAKE_CASE				,  _SCREAMING_SNAKE_CASE				,  _SCREAMING_SNAKE_CASE			)
  else:
    if sorted_collection[point] > item:
      return interpolation_search_by_recursion(
          _SCREAMING_SNAKE_CASE				,  _SCREAMING_SNAKE_CASE				,  _SCREAMING_SNAKE_CASE				,  point - 1			)
    else:
      return interpolation_search_by_recursion(
          _SCREAMING_SNAKE_CASE				,  _SCREAMING_SNAKE_CASE				,  point + 1				,  _SCREAMING_SNAKE_CASE			)



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: List[Any]			)							->      Optional[Any]:







  """simple docstring"""





  if collection != sorted(_SCREAMING_SNAKE_CASE			):
    raise ValueError("""Collection must be ascending sorted"""			)
  return True


if __name__ == "__main__":
   import sys
   __lowerCamelCase    :				int							     =	0
   if debug == 1:
      __lowerCamelCase    :				str							     =	[10, 30, 40, 45, 50, 66, 77, 93]
      try:
         __assert_sorted(collection)
      except ValueError:
         sys.exit('''Sequence must be ascending sorted to apply interpolation search''')
      __lowerCamelCase    :				Any							     =	67

   __lowerCamelCase    :				Any							     =	interpolation_search(collection, target)
   if result is not None:
      print(F"""{target} found at positions: {result}""")
   else:
      print('''Not found''')

import pickle
import unittest

import torch

from accelerate import Accelerator
from accelerate.state import AcceleratorState
from accelerate.test_utils import require_cpu







@require_cpu
class __snake_case       (		unittest.TestCase	):




   def 			__a		(					self    :       Any   ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__    							=   torch.nn.Linear(10 ,			10   )
     SCREAMING_SNAKE_CASE__    							=   torch.optim.SGD(model.parameters() ,			0.1   )
     SCREAMING_SNAKE_CASE__    							=   Accelerator()
     SCREAMING_SNAKE_CASE__    							=   accelerator.prepare(_lowercase   )
     try:
       pickle.loads(pickle.dumps(_lowercase   )   )
     except Exception as e:
       self.fail(f"""Accelerated optimizer pickling failed with {e}"""   )
     AcceleratorState._reset_state()
