

"""simple docstring"""






def  UpperCamelCase   (     _lowerCAmelCase       :  list[list[int]],					_lowerCAmelCase       :  list[list[int]]	)			->     list[list[int]]:
	_UpperCAmelCase      :							Tuple       =   []
	_UpperCAmelCase      :							Optional[int]       =   len(_lowerCAmelCase	)
	for i in range(_lowerCAmelCase	):
		_UpperCAmelCase      :							Dict       =   []
		for j in range(_lowerCAmelCase	):
			_UpperCAmelCase      :							Union[str, Any]       =   0
			for k in range(_lowerCAmelCase	):
				_UpperCAmelCase      :							Optional[Any]       =   val + matrix_a[i][k] * matrix_b[k][j]
			list_a.append(_lowerCAmelCase	)
		matrix_c.append(_lowerCAmelCase	)
	return matrix_c
def  UpperCamelCase   (     _lowerCAmelCase       :  int	)			->     list[list[int]]:
	return [[int(row == column	) for column in range(_lowerCAmelCase	)] for row in range(_lowerCAmelCase	)]
def  UpperCamelCase   (     _lowerCAmelCase       :  int	)			->     int:
	if n <= 1:
		return n
	_UpperCAmelCase      :							Any       =   identity(2	)
	_UpperCAmelCase      :							Any       =   [[1, 1], [1, 0]]
	_UpperCAmelCase      :							Optional[Any]       =   n - 1
	while n > 0:
		if n % 2 == 1:
			_UpperCAmelCase      :							Union[str, Any]       =   multiply(_lowerCAmelCase,					_lowerCAmelCase	)
		_UpperCAmelCase      :							int       =   multiply(_lowerCAmelCase,					_lowerCAmelCase	)
		_UpperCAmelCase      :							str       =   int(n / 2	)
	return res_matrix[0][0]
def  UpperCamelCase   (     _lowerCAmelCase       :  int	)			->     int:
	if n <= 1:
		return n
	_UpperCAmelCase      :							Dict       =   0
	_UpperCAmelCase      :							Tuple       =   1
	for _ in range(2,					n + 1	):
		_UpperCAmelCase  ,				_UpperCAmelCase      :							Optional[int]       =   fiba, fiba + fiba
	return fiba
def  UpperCamelCase   (     )			->     None:
	for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
		_UpperCAmelCase      :							Dict       =   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(_lowerCAmelCase	)} and using bruteforce is '''
		    f'''{nth_fibonacci_bruteforce(_lowerCAmelCase	)}\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"""






def  UpperCamelCase   (     _lowerCAmelCase       :  float,					_lowerCAmelCase       :  float,					_lowerCAmelCase       :  float	)			->     float:
	if mass < 0:
		raise ValueError("""The mass of the body cannot be negative"""	)
	if radius <= 0:
		raise ValueError("""The radius is always a positive non zero integer"""	)
	return (mass * (velocity) ** 2) / radius


if __name__ == "__main__":
						import doctest

						doctest.testmod(verbose=True)





