


import math







def   lowerCamelCase(      a__):

				if 1 < number < 4:
								# 2 and 3 are primes
								return True
				elif number < 2 or number % 2 == 0 or number % 3 == 0:
								# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
								return False

				# All primes number are in format of 6k +/- 1
				for i in range(5		,int(math.sqrt(a__) + 1)		,6):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True







def   lowerCamelCase(      a__ = 1000		,a__ = 1000):
				_SCREAMING_SNAKE_CASE	     =[0, 0, 0]  # length, a, b
				for a in range((a_limit * -1) + 1		,a__):
								for b in range(2		,a__):
												if is_prime(a__):
																_SCREAMING_SNAKE_CASE	     =0
																_SCREAMING_SNAKE_CASE	     =0
																while is_prime((n**2) + (a * n) + b):
																				count += 1
																				n += 1
																if count > longest[0]:
																				_SCREAMING_SNAKE_CASE	     =[count, a, b]
				_SCREAMING_SNAKE_CASE	     =longest[1] * longest[2]
				return ans


if __name__ == "__main__":
							print(solution(10_00, 10_00))





import csv
import os

import pytest

from datasets import Dataset, DatasetDict, Features, NamedSplit, Value
from datasets.io.csv import CsvDatasetReader, CsvDatasetWriter

from ..utils import assert_arrow_memory_doesnt_increase, assert_arrow_memory_increases







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase       )  ->str:






					"""simple docstring"""






					assert isinstance(UpperCAmelCase,	UpperCAmelCase       )
					assert dataset.num_rows == 4
					assert dataset.num_columns == 3
					assert dataset.column_names == ["col_1", "col_2", "col_3"]
					for feature, expected_dtype in expected_features.items():
										assert dataset.features[feature].dtype == expected_dtype







@pytest.mark.parametrize('''keep_in_memory''',	[False, True]       )
def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->Any:






					"""simple docstring"""






					__magic_name__					:							Dict		   =							tmp_path / '''cache'''
					__magic_name__					:							Tuple		   =							{'''col_1''': '''int64''', '''col_2''': '''int64''', '''col_3''': '''float64'''}
					with assert_arrow_memory_increases() if keep_in_memory else assert_arrow_memory_doesnt_increase():
										__magic_name__					:							str		   =							CsvDatasetReader(UpperCAmelCase,	cache_dir=UpperCAmelCase,	keep_in_memory=UpperCAmelCase       ).read()
					_check_csv_dataset(UpperCAmelCase,	UpperCAmelCase       )







@pytest.mark.parametrize(
    '''features''',	[
        None,
        {'''col_1''': '''string''', '''col_2''': '''int64''', '''col_3''': '''float64'''},
        {'''col_1''': '''string''', '''col_2''': '''string''', '''col_3''': '''string'''},
        {'''col_1''': '''int32''', '''col_2''': '''int32''', '''col_3''': '''int32'''},
        {'''col_1''': '''float32''', '''col_2''': '''float32''', '''col_3''': '''float32'''},
    ],	)
def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->Tuple:






					"""simple docstring"""






					__magic_name__					:							Tuple		   =							tmp_path / '''cache'''
					# CSV file loses col_1 string dtype information: default now is "int64" instead of "string"
					__magic_name__					:							List[Any]		   =							{'''col_1''': '''int64''', '''col_2''': '''int64''', '''col_3''': '''float64'''}
					__magic_name__					:							Tuple		   =							features.copy() if features else default_expected_features
					__magic_name__					:							str		   =							(
					    Features({feature: Value(UpperCAmelCase       ) for feature, dtype in features.items()}       ) if features is not None else None
					)
					__magic_name__					:							Dict		   =							CsvDatasetReader(UpperCAmelCase,	features=UpperCAmelCase,	cache_dir=UpperCAmelCase       ).read()
					_check_csv_dataset(UpperCAmelCase,	UpperCAmelCase       )







@pytest.mark.parametrize('''split''',	[None, NamedSplit('''train'''       ), '''train''', '''test''']       )
def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->List[Any]:






					"""simple docstring"""






					__magic_name__					:							str		   =							tmp_path / '''cache'''
					__magic_name__					:							List[str]		   =							{'''col_1''': '''int64''', '''col_2''': '''int64''', '''col_3''': '''float64'''}
					__magic_name__					:							int		   =							CsvDatasetReader(UpperCAmelCase,	cache_dir=UpperCAmelCase,	split=UpperCAmelCase       ).read()
					_check_csv_dataset(UpperCAmelCase,	UpperCAmelCase       )
					assert dataset.split == split if split else "train"







@pytest.mark.parametrize('''path_type''',	[str, list]       )
def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->str:






					"""simple docstring"""






					if issubclass(UpperCAmelCase,	UpperCAmelCase       ):
										__magic_name__					:							str		   =							csv_path
					elif issubclass(UpperCAmelCase,	UpperCAmelCase       ):
										__magic_name__					:							str		   =							[csv_path]
					__magic_name__					:							Optional[int]		   =							tmp_path / '''cache'''
					__magic_name__					:							Any		   =							{'''col_1''': '''int64''', '''col_2''': '''int64''', '''col_3''': '''float64'''}
					__magic_name__					:							Tuple		   =							CsvDatasetReader(UpperCAmelCase,	cache_dir=UpperCAmelCase       ).read()
					_check_csv_dataset(UpperCAmelCase,	UpperCAmelCase       )







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase=("train",)       )  ->Tuple:






					"""simple docstring"""






					assert isinstance(UpperCAmelCase,	UpperCAmelCase       )
					for split in splits:
										__magic_name__					:							int		   =							dataset_dict[split]
										assert dataset.num_rows == 4
										assert dataset.num_columns == 3
										assert dataset.column_names == ["col_1", "col_2", "col_3"]
										for feature, expected_dtype in expected_features.items():
															assert dataset.features[feature].dtype == expected_dtype







@pytest.mark.parametrize('''keep_in_memory''',	[False, True]       )
def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->int:






					"""simple docstring"""






					__magic_name__					:							Tuple		   =							tmp_path / '''cache'''
					__magic_name__					:							int		   =							{'''col_1''': '''int64''', '''col_2''': '''int64''', '''col_3''': '''float64'''}
					with assert_arrow_memory_increases() if keep_in_memory else assert_arrow_memory_doesnt_increase():
										__magic_name__					:							Optional[Any]		   =							CsvDatasetReader({'''train''': csv_path},	cache_dir=UpperCAmelCase,	keep_in_memory=UpperCAmelCase       ).read()
					_check_csv_datasetdict(UpperCAmelCase,	UpperCAmelCase       )







@pytest.mark.parametrize(
    '''features''',	[
        None,
        {'''col_1''': '''string''', '''col_2''': '''int64''', '''col_3''': '''float64'''},
        {'''col_1''': '''string''', '''col_2''': '''string''', '''col_3''': '''string'''},
        {'''col_1''': '''int32''', '''col_2''': '''int32''', '''col_3''': '''int32'''},
        {'''col_1''': '''float32''', '''col_2''': '''float32''', '''col_3''': '''float32'''},
    ],	)
def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->List[str]:






					"""simple docstring"""






					__magic_name__					:							Any		   =							tmp_path / '''cache'''
					# CSV file loses col_1 string dtype information: default now is "int64" instead of "string"
					__magic_name__					:							Dict		   =							{'''col_1''': '''int64''', '''col_2''': '''int64''', '''col_3''': '''float64'''}
					__magic_name__					:							Dict		   =							features.copy() if features else default_expected_features
					__magic_name__					:							Any		   =							(
					    Features({feature: Value(UpperCAmelCase       ) for feature, dtype in features.items()}       ) if features is not None else None
					)
					__magic_name__					:							List[str]		   =							CsvDatasetReader({'''train''': csv_path},	features=UpperCAmelCase,	cache_dir=UpperCAmelCase       ).read()
					_check_csv_datasetdict(UpperCAmelCase,	UpperCAmelCase       )







@pytest.mark.parametrize('''split''',	[None, NamedSplit('''train'''       ), '''train''', '''test''']       )
def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->List[str]:






					"""simple docstring"""






					if split:
										__magic_name__					:							Dict		   =							{split: csv_path}
					else:
										__magic_name__					:							Any		   =							{'''train''': csv_path, '''test''': csv_path}
					__magic_name__					:							str		   =							tmp_path / '''cache'''
					__magic_name__					:							Union[str, Any]		   =							{'''col_1''': '''int64''', '''col_2''': '''int64''', '''col_3''': '''float64'''}
					__magic_name__					:							int		   =							CsvDatasetReader(UpperCAmelCase,	cache_dir=UpperCAmelCase       ).read()
					_check_csv_datasetdict(UpperCAmelCase,	UpperCAmelCase,	splits=list(path.keys()       )       )
					assert all(dataset[split].split == split for split in path.keys()       )







def  lowerCAmelCase  (	UpperCAmelCase       )  ->int:






					"""simple docstring"""






					with open(UpperCAmelCase,	encoding='''utf-8'''       ) as csvfile:
										yield from csv.reader(UpperCAmelCase       )







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase       )  ->int:






					"""simple docstring"""






					__magic_name__					:							Dict		   =							tmp_path / '''cache'''
					__magic_name__					:							List[Any]		   =							os.path.join(UpperCAmelCase,	'''tmp.csv'''       )
					__magic_name__					:							int		   =							CsvDatasetReader({'''train''': csv_path},	cache_dir=UpperCAmelCase       ).read()
					CsvDatasetWriter(dataset['''train'''],	UpperCAmelCase,	num_proc=1       ).write()

					__magic_name__					:							Optional[int]		   =							iter_csv_file(UpperCAmelCase       )
					__magic_name__					:							Any		   =							iter_csv_file(UpperCAmelCase       )

					for rowa, rowa in zip(UpperCAmelCase,	UpperCAmelCase       ):
										assert rowa == rowa







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase       )  ->Union[str, Any]:






					"""simple docstring"""






					__magic_name__					:							Optional[int]		   =							tmp_path / '''cache'''
					__magic_name__					:							Optional[Any]		   =							os.path.join(UpperCAmelCase,	'''tmp.csv'''       )
					__magic_name__					:							List[Any]		   =							CsvDatasetReader({'''train''': csv_path},	cache_dir=UpperCAmelCase       ).read()
					CsvDatasetWriter(dataset['''train'''],	UpperCAmelCase,	num_proc=2       ).write()

					__magic_name__					:							Tuple		   =							iter_csv_file(UpperCAmelCase       )
					__magic_name__					:							List[str]		   =							iter_csv_file(UpperCAmelCase       )

					for rowa, rowa in zip(UpperCAmelCase,	UpperCAmelCase       ):
										assert rowa == rowa







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase       )  ->int:






					"""simple docstring"""






					__magic_name__					:							Optional[int]		   =							tmp_path / '''cache'''
					__magic_name__					:							Any		   =							os.path.join(UpperCAmelCase,	'''tmp.csv'''       )
					__magic_name__					:							Any		   =							CsvDatasetReader({'''train''': csv_path},	cache_dir=UpperCAmelCase       ).read()
					with pytest.raises(UpperCAmelCase       ):
										CsvDatasetWriter(dataset['''train'''],	UpperCAmelCase,	num_proc=0       )



