def  _lowerCamelCase					(   a_				: int):
			lowerCamelCase						:int						  =     (1 + 24 * n) ** 0.5
			return ((1 + root) / 6) % 1 == 0





def  _lowerCamelCase					(   a_				: int = 50_00):
			lowerCamelCase						:Union[str, Any]						  =     [(i * (3 * i - 1)) // 2 for i in range(1						,			a_)]
			for i, pentagonal_i in enumerate(a_):
						for j in range(a_						,			len(a_)):
									lowerCamelCase						:Dict						  =     pentagonal_nums[j]
									lowerCamelCase						:Any						  =     pentagonal_i + pentagonal_j
									lowerCamelCase						:str						  =     pentagonal_j - pentagonal_i
									if is_pentagonal(a_) and is_pentagonal(a_):
												return b

			return -1


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




import os
from typing import Optional

import fsspec
from fsspec.archive import AbstractArchiveFileSystem
from fsspec.utils import DEFAULT_BLOCK_SIZE
class   _lowerCAmelCase		(     __SCREAMING_SNAKE_CASE				):
							_UpperCAmelCase						    =     ''
							_UpperCAmelCase						    =     (
							    None  # protocol passed in prefix to the url. ex: "gzip", for gzip://file.txt::http://foo.bar/file.txt.gz
							)
							_UpperCAmelCase						    =     None  # compression type in fsspec. ex: "gzip"
							_UpperCAmelCase						    =     None  # extension of the filename to strip. ex: "".gz" to get file.txt from file.txt.gz







							def __init__(				self     :    str	,					__snake_case     :    str = ""	,					__snake_case     :    Optional[str] = None	,					__snake_case     :    Optional[dict] = None	,					**__snake_case     :    Dict		):
										super().__init__(self	,					**__snake_case		)
										# always open as "rb" since fsspec can then use the TextIOWrapper to make it work for "r" mode
										lowerCamelCase						:Optional[Any]						  =     fsspec.open(
										    __snake_case	,					mode='''rb'''	,					protocol=__snake_case	,					compression=self.compression	,					client_kwargs={
										        '''requote_redirect_url''': False,  # see https://github.com/huggingface/datasets/pull/5459
										        '''trust_env''': True,  # Enable reading proxy env variables.
										        **(target_options or {}).pop('''client_kwargs'''	,					{}		),  # To avoid issues if it was already passed.
										    }	,					**(target_options or {})	,					)
										lowerCamelCase						:List[str]						  =     os.path.basename(self.file.path.split('''::'''		)[0]		)
										lowerCamelCase						:Dict						  =     (
										    self.compressed_name[: self.compressed_name.rindex('''.'''		)]
										    if '''.''' in self.compressed_name
										    else self.compressed_name
										)
										lowerCamelCase						:List[str]						  =     None







							@classmethod
							def 				snake_case  (				cls     :    Any	,					__snake_case     :    Any		):
										# compressed file paths are always relative to the archive root
										return super()._strip_protocol(__snake_case		).lstrip('''/'''		)







							def 				snake_case  (				self     :    Any		):
										if self.dir_cache is None:
													lowerCamelCase						:Optional[Any]						  =     {**self.file.fs.info(self.file.path		), '''name''': self.uncompressed_name}
													lowerCamelCase						:Optional[Any]						  =     {f['''name''']: f}







							def 				snake_case  (				self     :    Union[str, Any]	,					__snake_case     :    str		):
										return self.file.open().read()







							def 				snake_case  (				self     :    Optional[int]	,					__snake_case     :    str	,					__snake_case     :    str = "rb"	,					__snake_case     :    int=None	,					__snake_case     :    Optional[int]=True	,					__snake_case     :    str=None	,					**__snake_case     :    str	,					):
										lowerCamelCase						:List[str]						  =     self._strip_protocol(__snake_case		)
										if mode != "rb":
													raise ValueError(F"Tried to read with mode {mode} on file {self.file.path} opened with mode 'rb'"		)
										return self.file.open()


class   _lowerCAmelCase		(     __SCREAMING_SNAKE_CASE				):
							_UpperCAmelCase						    =     'bz2'
							_UpperCAmelCase						    =     'bz2'
							_UpperCAmelCase						    =     '.bz2'


class   _lowerCAmelCase		(     __SCREAMING_SNAKE_CASE				):
							_UpperCAmelCase						    =     'gzip'
							_UpperCAmelCase						    =     'gzip'
							_UpperCAmelCase						    =     '.gz'


class   _lowerCAmelCase		(     __SCREAMING_SNAKE_CASE				):
							_UpperCAmelCase						    =     'lz4'
							_UpperCAmelCase						    =     'lz4'
							_UpperCAmelCase						    =     '.lz4'


class   _lowerCAmelCase		(     __SCREAMING_SNAKE_CASE				):
							_UpperCAmelCase						    =     'xz'
							_UpperCAmelCase						    =     'xz'
							_UpperCAmelCase						    =     '.xz'


class   _lowerCAmelCase		(     __SCREAMING_SNAKE_CASE				):
							_UpperCAmelCase						    =     'zstd'
							_UpperCAmelCase						    =     'zstd'
							_UpperCAmelCase						    =     '.zst'







							def __init__(				self     :    str	,					__snake_case     :    str	,					__snake_case     :    str = "rb"	,					__snake_case     :    Optional[str] = None	,					__snake_case     :    Optional[dict] = None	,					__snake_case     :    int = DEFAULT_BLOCK_SIZE	,					**__snake_case     :    int	,					):
										super().__init__(
										    fo=__snake_case	,					mode=__snake_case	,					target_protocol=__snake_case	,					target_options=__snake_case	,					block_size=__snake_case	,					**__snake_case	,					)
										# We need to wrap the zstd decompressor to avoid this error in fsspec==2021.7.0 and zstandard==0.15.2:
										#
										# File "/Users/user/.virtualenvs/hf-datasets/lib/python3.7/site-packages/fsspec/core.py", line 145, in open
										#     out.close = close
										# AttributeError: 'zstd.ZstdDecompressionReader' object attribute 'close' is read-only
										#
										# see https://github.com/intake/filesystem_spec/issues/725
										lowerCamelCase						:Tuple						  =     self.file.__enter__
										class   _lowerCAmelCase		:







																	def __init__(				self     :    Dict	,					__snake_case     :    Tuple		):
																				lowerCamelCase						:Optional[int]						  =     file_







																	def __enter__(				self     :    Optional[int]		):
																				self._file.__enter__()
																				return self







																	def __exit__(				self     :    str	,					*__snake_case     :    Optional[Any]	,					**__snake_case     :    List[Any]		):
																				self._file.__exit__(*__snake_case	,					**__snake_case		)







																	def __iter__(				self     :    Optional[Any]		):
																				return iter(self._file		)







																	def 				snake_case  (				self     :    List[Any]		):
																				return next(self._file		)







																	def __getattr__(				self     :    Any	,					__snake_case     :    str		):
																				return getattr(self._file	,					__snake_case		)

										def fixed_enter(*__snake_case     :    Optional[int]	,					**__snake_case     :    str		):
													return WrappedFile(_enter(*__snake_case	,					**__snake_case		)		)

										lowerCamelCase						:Dict						  =     fixed_enter



