


import math






def 		_A		(		_lowercase					,  _lowercase )					-> float:


     """simple docstring"""


     return math.pow(_lowercase					,  2 ) - a






def 		_A		(		_lowercase )					-> float:


     """simple docstring"""


     return 2 * x






def 		_A		(		_lowercase )					-> float:


     """simple docstring"""


     __UpperCamelCase =			2.0

     while start <= a:
          __UpperCamelCase =			math.pow(_lowercase					,  2 )

     return start






def 		_A		(		_lowercase					,  _lowercase = 99_99					,  _lowercase = 0.00_00_00_00_00_00_01 )					-> float:


     """simple docstring"""


     if a < 0:
          raise ValueError('math domain error' )

     __UpperCamelCase =			get_initial_point(_lowercase )

     for _ in range(_lowercase ):
          __UpperCamelCase =			value
          __UpperCamelCase =			value - fx(_lowercase					,  _lowercase ) / fx_derivative(_lowercase )
          if abs(prev_value - value ) < tolerance:
               return value

     return value


if __name__ == "__main__":
    from doctest import testmod

    testmod()








from collections.abc import Iterator, MutableMapping
from dataclasses import dataclass
from typing import Generic, TypeVar

__magic_name__  :  Any					=       TypeVar("""KEY""")
__magic_name__  :  Dict					=       TypeVar("""VAL""")





@dataclass(frozen=_a    ,					slots=_a			)
class     SCREAMING_SNAKE_CASE__		(Generic[KEY, VAL]			):
     lowercase_ :      KEY
     lowercase_ :      VAL





class     SCREAMING_SNAKE_CASE__		(_Item			):
     def __init__(						self	:		Tuple						):



       """simple docstring"""
       super().__init__(__lowerCamelCase       ,						__lowerCamelCase						)



     def __bool__(						self	:		Tuple						):



       """simple docstring"""
       return False



__magic_name__  :  str					=       _DeletedItem()





class     SCREAMING_SNAKE_CASE__		(MutableMapping[KEY, VAL]			):
     def __init__(						self	:		Any       ,						__lowerCamelCase	:		int = 8       ,						__lowerCamelCase	:		float = 0.75						):



       """simple docstring"""
       lowerCAmelCase__										=      initial_block_size
       lowerCAmelCase__										=      [None] * initial_block_size
       assert 0.0 < capacity_factor < 1.0
       lowerCAmelCase__										=      capacity_factor
       lowerCAmelCase__										=      0
     def        A__      (						self	:		Union[str, Any]       ,						__lowerCamelCase	:		KEY						):



       """simple docstring"""
       return hash(__lowerCamelCase						) % len(self._buckets						)
     def        A__      (						self	:		Tuple       ,						__lowerCamelCase	:		int						):



       """simple docstring"""
       return (ind + 1) % len(self._buckets						)
     def        A__      (						self	:		Dict       ,						__lowerCamelCase	:		int       ,						__lowerCamelCase	:		KEY       ,						__lowerCamelCase	:		VAL						):



       """simple docstring"""
       lowerCAmelCase__										=      self._buckets[ind]
       if not stored:
         lowerCAmelCase__										=      _Item(__lowerCamelCase       ,						__lowerCamelCase						)
         self._len += 1
         return True
       elif stored.key == key:
         lowerCAmelCase__										=      _Item(__lowerCamelCase       ,						__lowerCamelCase						)
         return True
       else:
         return False
     def        A__      (						self	:		Any						):



       """simple docstring"""
       lowerCAmelCase__										=      len(self._buckets						) * self._capacity_factor
       return len(self						) >= int(__lowerCamelCase						)
     def        A__      (						self	:		Tuple						):



       """simple docstring"""
       if len(self._buckets						) <= self._initial_block_size:
         return False
       lowerCAmelCase__										=      len(self._buckets						) * self._capacity_factor / 2
       return len(self						) < limit
     def        A__      (						self	:		List[Any]       ,						__lowerCamelCase	:		int						):



       """simple docstring"""
       lowerCAmelCase__										=      self._buckets
       lowerCAmelCase__										=      [None] * new_size
       lowerCAmelCase__										=      0
       for item in old_buckets:
         if item:
           self._add_item(item.key       ,						item.val						)
     def        A__      (						self	:		Any						):



       """simple docstring"""
       self._resize(len(self._buckets						) * 2						)
     def        A__      (						self	:		Dict						):



       """simple docstring"""
       self._resize(len(self._buckets						) // 2						)
     def        A__      (						self	:		List[str]       ,						__lowerCamelCase	:		KEY						):



       """simple docstring"""
       lowerCAmelCase__										=      self._get_bucket_index(__lowerCamelCase						)
       for _ in range(len(self._buckets						)						):
         yield ind
         lowerCAmelCase__										=      self._get_next_ind(__lowerCamelCase						)
     def        A__      (						self	:		Dict       ,						__lowerCamelCase	:		KEY       ,						__lowerCamelCase	:		VAL						):



       """simple docstring"""
       for ind in self._iterate_buckets(__lowerCamelCase						):
         if self._try_set(__lowerCamelCase       ,						__lowerCamelCase       ,						__lowerCamelCase						):
           break
     def __setitem__(						self	:		str       ,						__lowerCamelCase	:		KEY       ,						__lowerCamelCase	:		VAL						):



       """simple docstring"""
       if self._is_full():
         self._size_up()

       self._add_item(__lowerCamelCase       ,						__lowerCamelCase						)
     def __delitem__(						self	:		Tuple       ,						__lowerCamelCase	:		KEY						):



       """simple docstring"""
       for ind in self._iterate_buckets(__lowerCamelCase						):
         lowerCAmelCase__										=      self._buckets[ind]
         if item is None:
           raise KeyError(__lowerCamelCase						)
         if item is _deleted:
           continue
         if item.key == key:
           lowerCAmelCase__										=      _deleted
           self._len -= 1
           break
       if self._is_sparse():
         self._size_down()
     def __getitem__(						self	:		Optional[int]       ,						__lowerCamelCase	:		KEY						):



       """simple docstring"""
       for ind in self._iterate_buckets(__lowerCamelCase						):
         lowerCAmelCase__										=      self._buckets[ind]
         if item is None:
           break
         if item is _deleted:
           continue
         if item.key == key:
           return item.val
       raise KeyError(__lowerCamelCase						)
     def __len__(						self	:		int						):



       """simple docstring"""
       return self._len
     def __iter__(						self	:		Union[str, Any]						):



       """simple docstring"""
       yield from (item.key for item in self._buckets if item)



     def __repr__(						self	:		Union[str, Any]						):



       """simple docstring"""
       lowerCAmelCase__										=      ''' ,'''.join(
           F"""{item.key}: {item.val}""" for item in self._buckets if item						)
       return F"""HashMap({val_string})"""

