code: 
  
  
  """simple docstring"""
  
  
  
  
  def 			a_   (  lowercase__   :list[list[int]], lowercase__   :list[list[int]]    ):
  			__lowerCamelCase        =			[]
  			__lowerCamelCase        =			len(lowercase__    )
  			for i in range(lowercase__    ):
  						__lowerCamelCase        =			[]
  						for j in range(lowercase__    ):
  									__lowerCamelCase        =			0
  									for k in range(lowercase__    ):
  												__lowerCamelCase        =			val + matrix_a[i][k] * matrix_b[k][j]
  									list_a.append(lowercase__    )
  						matrix_c.append(lowercase__    )
  			return matrix_c
  
  
  
  
  
  def 			a_   (  lowercase__   :int    ):
  			return [[int(row == column    ) for column in range(lowercase__    )] for row in range(lowercase__    )]
  
  
  
  
  
  def 			a_   (  lowercase__   :int    ):
  			if n <= 1:
  						return n
  			__lowerCamelCase        =			identity(2    )
  			__lowerCamelCase        =			[[1, 1], [1, 0]]
  			__lowerCamelCase        =			n - 1
  			while n > 0:
  						if n % 2 == 1:
  									__lowerCamelCase        =			multiply(lowercase__, lowercase__    )
  						__lowerCamelCase        =			multiply(lowercase__, lowercase__    )
  						__lowerCamelCase        =			int(n / 2    )
  			return res_matrix[0][0]
  
  
  
  
  
  def 			a_   (  lowercase__   :int    ):
  			if n <= 1:
  						return n
  			__lowerCamelCase        =			0
  			__lowerCamelCase        =			1
  			for _ in range(2, n + 1    ):
  						__lowerCamelCase    ,__lowerCamelCase        =			fiba, fiba + fiba
  			return fiba
  
  
  
  
  
  def 			a_   (  ):
  			for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
  						__lowerCamelCase        =			int("""""".join(c for c in ordinal if c in """0123456789"""    )    )  # 1000th --> 1000
  						print(
  						    f'{ordinal} fibonacci number using matrix exponentiation is '
  						    f'{nth_fibonacci_matrix(lowercase__    )} and using bruteforce is '
  						    f'{nth_fibonacci_bruteforce(lowercase__    )}\n'    )
  			# from timeit import timeit
  			# print(timeit("nth_fibonacci_matrix(1000000)",
  			#              "from main import nth_fibonacci_matrix", number=5))
  			# print(timeit("nth_fibonacci_bruteforce(1000000)",
  			#              "from main import nth_fibonacci_bruteforce", number=5))
  			# 2.3342058970001744
  			# 57.256506615000035
  
  
  if __name__ == "__main__":
  		import doctest
  
  		doctest.testmod()
  		main()
  
  
  
  
  
style_context: 
  
  
  """simple docstring"""
  
  
  
  
  # Lint as: python3
  
  import hashlib
  from typing import Union
  
  
  
  
  
  def 			a_   (  lowercase__   :Union[str, int, bytes]    ):
  			if isinstance(lowercase__, lowercase__    ):
  						# Data already in bytes, returns as it as
  						return hash_data
  			elif isinstance(lowercase__, lowercase__    ):
  						# We keep the data as it as for it ot be later encoded to UTF-8
  						# However replace `\\` with `/` for Windows compatibility
  						__lowerCamelCase        =			hash_data.replace("""\\""", """/"""    )
  			elif isinstance(lowercase__, lowercase__    ):
  						__lowerCamelCase        =			str(lowercase__    )
  			else:
  						# If data is not of the required type, raise error
  						raise InvalidKeyError(lowercase__    )
  
  			return hash_data.encode("""utf-8"""    )
  
  
  
  
  class  __snake_case      (lowerCamelCase     ):
  
  
  
  
  							def __init__(    self:						Union[str, Any]    ,       A_:						Tuple      ):
  										__lowerCamelCase        =			"""\nFAILURE TO GENERATE DATASET: Invalid key type detected"""
  										__lowerCamelCase        =			f'\nFound Key {hash_data} of type {type(A_      )}'
  										__lowerCamelCase        =			"""\nKeys should be either str, int or bytes type"""
  										super().__init__(f'{self.prefix}{self.err_msg}{self.suffix}'      )
  
  
  
  
  class  __snake_case      (lowerCamelCase     ):
  
  
  
  
  							def __init__(    self:						Any    ,       A_:						Dict    ,       A_:						List[Any]    ,       A_:						List[str]=""      ):
  										__lowerCamelCase        =			key
  										__lowerCamelCase        =			duplicate_key_indices
  										__lowerCamelCase        =			fix_msg
  										__lowerCamelCase        =			"""Found multiple examples generated with the same key"""
  										if len(A_      ) <= 20:
  													__lowerCamelCase        =			f'\nThe examples at index {", ".join(A_      )} have the key {key}'
  										else:
  													__lowerCamelCase        =			f'\nThe examples at index {", ".join(duplicate_key_indices[:20]      )}... ({len(A_      ) - 20} more) have the key {key}'
  										__lowerCamelCase        =			"""\n""" + fix_msg if fix_msg else """"""
  										super().__init__(f'{self.prefix}{self.err_msg}{self.suffix}'      )
  
  
  
  
  class  __snake_case      :
  
  
  
  
  							def __init__(    self:						Dict    ,       A_:						str      ):
  										__lowerCamelCase        =			hashlib.mda(_as_bytes(A_      )      )
  
  
  
  
  							def      __a      (    self:						int    ,       A_:						Union[str, int, bytes]      ):
  										__lowerCamelCase        =			self._split_mda.copy()
  										__lowerCamelCase        =			_as_bytes(A_      )
  										mda.update(A_      )
  										# Convert to integer with hexadecimal conversion
  										return int(mda.hexdigest()    ,       16      )
  
  
  
  
  