



"""simple docstring"""






def 	snake_case__  (						__lowerCamelCase							:       int = 998001      ):
			"""simple docstring"""

			# fetches the next number
			for number in range(n - 1				,						9999				,						-1      ):
						lowerCamelCase__						:						Optional[int]						      =str(__lowerCamelCase      )

						# checks whether 'str_number' is a palindrome.
						if str_number == str_number[::-1]:
									lowerCamelCase__						:						Optional[int]						      =999

									# 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() = }')












"""simple docstring"""




import math






def 							lowerCAmelCase			(   UpperCamelCase_:				int       )							->				list:







  '''simple docstring'''







  if n <= 0:
    raise ValueError("Only positive integers have prime factors"       )
  _a					      =						[]
  while n % 2 == 0:
    pf.append(2       )
    _a					      =						int(n / 2       )
  for i in range(3  ,			int(math.sqrt(UpperCamelCase_       )       ) + 1  ,			2       ):
    while n % i == 0:
      pf.append(UpperCamelCase_       )
      _a					      =						int(n / i       )
  if n > 2:
    pf.append(UpperCamelCase_       )
  return pf






def 							lowerCAmelCase			(   UpperCamelCase_:				int       )							->				int:







  '''simple docstring'''







  if n <= 0:
    raise ValueError("Only positive numbers are accepted"       )
  _a					      =						1
  _a					      =						1
  while n % 2 == 0:
    temp += 1
    _a					      =						int(n / 2       )
  div *= temp
  for i in range(3  ,			int(math.sqrt(UpperCamelCase_       )       ) + 1  ,			2       ):
    _a					      =						1
    while n % i == 0:
      temp += 1
      _a					      =						int(n / i       )
    div *= temp
  if n > 1:
    div *= 2
  return div






def 							lowerCAmelCase			(   UpperCamelCase_:				int       )							->				int:







  '''simple docstring'''







  if n <= 0:
    raise ValueError("Only positive numbers are accepted"       )
  _a					      =						1
  _a					      =						1
  while n % 2 == 0:
    temp += 1
    _a					      =						int(n / 2       )
  if temp > 1:
    s *= (2**temp - 1) / (2 - 1)
  for i in range(3  ,			int(math.sqrt(UpperCamelCase_       )       ) + 1  ,			2       ):
    _a					      =						1
    while n % i == 0:
      temp += 1
      _a					      =						int(n / i       )
    if temp > 1:
      s *= (i**temp - 1) / (i - 1)
  return int(UpperCamelCase_       )






def 							lowerCAmelCase			(   UpperCamelCase_:				int       )							->				int:







  '''simple docstring'''







  _a					      =						n
  for x in set(prime_factors(UpperCamelCase_       )       ):
    s *= (x - 1) / x
  return int(UpperCamelCase_       )


if __name__ == "__main__":
     import doctest

     doctest.testmod()


