


'''simple docstring'''



def 			_a			(		_lowercase      :			int						):





     '''simple docstring'''






     if not isinstance(_lowercase    ,      _lowercase						):
          __UpperCAmelCase			:				int													=    F'Input value of [number={number}] must be an integer'
          raise TypeError(_lowercase						)
     if number < 0:
          return False
     __UpperCAmelCase			:				List[Any]													=    number * number
     while number > 0:
          if number % 10 != number_square % 10:
               return False
          number //= 10
          number_square //= 10
     return True


if __name__ == "__main__":
      import doctest

      doctest.testmod()



'''simple docstring'''



from __future__ import annotations




def 			_a			(		_lowercase      :			int						):





     '''simple docstring'''






     __UpperCAmelCase			:				str													=    [True] * limit
     __UpperCAmelCase			:				Tuple													=    False
     __UpperCAmelCase			:				List[str]													=    False
     __UpperCAmelCase			:				List[Any]													=    True

     for i in range(3    ,      int(limit**0.5 + 1						)    ,      2						):
          __UpperCAmelCase			:				Dict													=    i * 2
          while index < limit:
               __UpperCAmelCase			:				Optional[int]													=    False
               __UpperCAmelCase			:				Union[str, Any]													=    index + i

     __UpperCAmelCase			:				Optional[Any]													=    [2]

     for i in range(3    ,      _lowercase    ,      2						):
          if is_prime[i]:
               primes.append(_lowercase						)

     return primes




def 			_a			(		_lowercase      :			int = 1000000						):





     '''simple docstring'''






     __UpperCAmelCase			:				List[str]													=    prime_sieve(_lowercase						)
     __UpperCAmelCase			:				Optional[Any]													=    0
     __UpperCAmelCase			:				int													=    0

     for i in range(len(_lowercase						)						):
          for j in range(i + length    ,      len(_lowercase						)						):
               __UpperCAmelCase			:				Optional[Any]													=    sum(primes[i:j]						)
               if sol >= ceiling:
                    break

               if sol in primes:
                    __UpperCAmelCase			:				Any													=    j - i
                    __UpperCAmelCase			:				List[Any]													=    sol

     return largest


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