





from functools import lru_cache





@lru_cache
def    _lowercase    (  _UpperCAmelCase )  ->     int:
				if not isinstance(_UpperCAmelCase	,					_UpperCAmelCase ):
								raise TypeError("""k must be an integer.""" )
				if k < 0:
								raise ValueError("""k integer must be greater or equal to zero.""" )
				if k == 0:
								return 0
				elif k == 1:
								return 1
				else:
								return fibonacci(k - 1 ) + fibonacci(k - 2 )





def    _lowercase    (  _UpperCAmelCase	,					_UpperCAmelCase )  ->     int:
				lowerCamelCase		       =len(_UpperCAmelCase )
				# Find m such that F_m >= n where F_i is the i_th fibonacci number.
				lowerCamelCase		       =0
				while True:
								if fibonacci(_UpperCAmelCase ) >= len_list:
												lowerCamelCase		       =i
												break
								i += 1
				lowerCamelCase		       =0
				while fibb_k > 0:
								lowerCamelCase		       =min(
								    offset + fibonacci(fibb_k - 1 )	,					len_list - 1 )  # Prevent out of range
								lowerCamelCase		       =arr[index_k]
								if item_k_1 == val:
												return index_k
								elif val < item_k_1:
												fibb_k -= 1
								elif val > item_k_1:
												offset += fibonacci(fibb_k - 1 )
												fibb_k -= 2
				else:
								return -1


if __name__ == "__main__":
							import doctest

							doctest.testmod()












def    _lowercase    (  _UpperCAmelCase = 99_80_01 )  ->     int:

				# fetches the next number
				for number in range(n - 1	,					99_99	,					-1 ):
								lowerCamelCase		       =str(_UpperCAmelCase )

								# checks whether 'str_number' is a palindrome.
								if str_number == str_number[::-1]:
												lowerCamelCase		       =9_99

												# if 'number' is a product of two 3-digit numbers
												# then number is the answer otherwise fetch next number.
												while divisor != 99:
																if (number % divisor == 0) and (len(str(number // divisor ) ) == 3.0):
																				return number
																divisor -= 1
				raise ValueError("""That number is larger than our acceptable range.""" )


if __name__ == "__main__":
							print(F"{solution() = }")





