






def      _lowerCamelCase	(						__A    :							str )      ->					str:
    _UpperCAmelCase				:      Tuple			  =				0

    # if input_string is "aba" than new_input_string become "a|b|a"
    _UpperCAmelCase				:      Union[str, Any]			  =				''''''
    _UpperCAmelCase				:      Dict			  =				''''''

    # append each character + "|" in new_string for range(0, length-1)
    for i in input_string[: len(__A ) - 1]:
        new_input_string += i + "|"
    # append last character
    new_input_string += input_string[-1]

    # we will store the starting and ending of previous furthest ending palindromic
    # substring
    _UpperCAmelCase  , _UpperCAmelCase				:      List[Any]			  =				0, 0

    # length[i] shows the length of palindromic substring with center i
    _UpperCAmelCase				:      Dict			  =				[1 for i in range(len(__A ) )]

    # for each character in new_string find corresponding palindromic string
    _UpperCAmelCase				:      Dict			  =				0
    for j in range(len(__A ) ):
        _UpperCAmelCase				:      str			  =				1 if j > r else min(length[l + r - j] // 2		,		r - j + 1 )
        while (
            j - k >= 0
            and j + k < len(__A )
            and new_input_string[k + j] == new_input_string[j - k]
        ):
            k += 1

        _UpperCAmelCase				:      int			  =				2 * k - 1

        # does this string is ending after the previously explored end (that is r) ?
        # if yes the update the new r to the last index of this
        if j + k - 1 > r:
            _UpperCAmelCase				:      Union[str, Any]			  =				j - k + 1  # noqa: E741
            _UpperCAmelCase				:      Optional[int]			  =				j + k - 1

        # update max_length and start position
        if max_length < length[j]:
            _UpperCAmelCase				:      Tuple			  =				length[j]
            _UpperCAmelCase				:      List[Any]			  =				j

    # create that string
    _UpperCAmelCase				:      Tuple			  =				new_input_string[start - max_length // 2 : start + max_length // 2 + 1]
    for i in s:
        if i != "|":
            output_string += i

    return output_string


if __name__ == "__main__":
  import doctest

  doctest.testmod()












from __future__ import annotations

def      _lowerCamelCase	(						__A    :							int )      ->					list[int]:
    _UpperCAmelCase				:      List[str]			  =				[True] * limit
    _UpperCAmelCase				:      Optional[int]			  =				False
    _UpperCAmelCase				:      Dict			  =				False
    _UpperCAmelCase				:      List[str]			  =				True

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

    _UpperCAmelCase				:      Optional[int]			  =				[2]

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

    return primes

def      _lowerCamelCase	(						__A    :							int = 1_000_000 )      ->					int:
    _UpperCAmelCase				:      Any			  =				prime_sieve(__A )
    _UpperCAmelCase				:      Optional[Any]			  =				0
    _UpperCAmelCase				:      Tuple			  =				0

    for i in range(len(__A ) ):
        for j in range(i + length		,		len(__A ) ):
            _UpperCAmelCase				:      List[Any]			  =				sum(primes[i:j] )
            if sol >= ceiling:
                break

            if sol in primes:
                _UpperCAmelCase				:      List[str]			  =				j - i
                _UpperCAmelCase				:      Optional[Any]			  =				sol

    return largest


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




