


"""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()








"""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      )




