


"""simple docstring"""






def 			A__		(					_UpperCAmelCase    :      str				,    _UpperCAmelCase    :      str	)							->	Tuple:

	'''simple docstring'''


	snake_case__  :						Optional[Any]		=      []
	snake_case__  :						Optional[Any]		=      len(_UpperCAmelCase	)
	for i in range(_UpperCAmelCase	):
		snake_case__  :						Union[str, Any]		=      []
		for j in range(_UpperCAmelCase	):
			snake_case__  :						Dict		=      0
			for k in range(_UpperCAmelCase	):
				snake_case__  :						Any		=      val + matrix_a[i][k] * matrix_b[k][j]
			list_a.append(_UpperCAmelCase	)
		matrix_c.append(_UpperCAmelCase	)
	return matrix_c



def 			A__		(					_UpperCAmelCase    :      Union[str, Any]	)							->	Tuple:

	'''simple docstring'''


	return [[int(row == column	) for column in range(_UpperCAmelCase	)] for row in range(_UpperCAmelCase	)]



def 			A__		(					_UpperCAmelCase    :      int	)							->	List[str]:

	'''simple docstring'''


	if n <= 1:
		return n
	snake_case__  :						Tuple		=      identity(2	)
	snake_case__  :						Union[str, Any]		=      [[1, 1], [1, 0]]
	snake_case__  :						str		=      n - 1
	while n > 0:
		if n % 2 == 1:
			snake_case__  :						List[str]		=      multiply(_UpperCAmelCase				,    _UpperCAmelCase	)
		snake_case__  :						str		=      multiply(_UpperCAmelCase				,    _UpperCAmelCase	)
		snake_case__  :						Dict		=      int(n / 2	)
	return res_matrix[0][0]



def 			A__		(					_UpperCAmelCase    :      List[Any]	)							->	Dict:

	'''simple docstring'''


	if n <= 1:
		return n
	snake_case__  :						Dict		=      0
	snake_case__  :						str		=      1
	for _ in range(2				,    n + 1	):
		snake_case__,					snake_case__  :						Optional[Any]		=      fiba, fiba + fiba
	return fiba



def 			A__		(					)							->	str:

	'''simple docstring'''


	for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
		snake_case__  :						List[Any]		=      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(_UpperCAmelCase	)} and using bruteforce is """
		    F"""{nth_fibonacci_bruteforce(_UpperCAmelCase	)}\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()










def 	__snake_case      (     _UpperCAmelCase							):
    __a					=							1
    __a					=							0
    __a					=							1
    __a					=							1
    __a					=							3
    __a					=							3
    __a					=							limit
    __a					=							0

    __a					=							''''''
    while counter != decimal + 1:
        if 4 * q + r - t < n * t:
            result += str(_UpperCAmelCase							)
            if counter == 0:
                result += "."

            if decimal == counter:
                break

            counter += 1
            __a					=							10 * (r - n * t)
            __a					=							((10 * (3 * q + r)) // t) - 10 * n
            q *= 10
            __a					=							nr
        else:
            __a					=							(2 * q + r) * l
            __a					=							(q * (7 * k) + 2 + (r * l)) // (t * l)
            q *= k
            t *= l
            l += 2
            k += 1
            __a					=							nn
            __a					=							nr
    return result





def 	__snake_case      (     ):
    print(f'{calculate_pi(50							) = }'							)
    import doctest

    doctest.testmod()


if __name__ == "__main__":
 main()





