


'''simple docstring'''

import math
from itertools import permutations





def lowerCamelCase    (    lowerCAmelCase       :			Optional[Any]	):





		"""simple docstring"""







		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(lowerCamelCase__	) + 1	)	,	6	):
				if number % i == 0 or number % (i + 2) == 0:
						return False
		return True





def lowerCamelCase    (    lowerCAmelCase       :			Dict	,	lowerCAmelCase       :			str	):





		"""simple docstring"""







		__magic_name__			,       __magic_name__ :					Any  			=  0, len(lowerCamelCase__	) - 1
		while left <= right:
				__magic_name__ :					Dict  			=  (left + right) // 2
				if prime_list[middle] == target:
						return True
				elif prime_list[middle] < target:
						__magic_name__ :					int  			=  middle + 1
				else:
						__magic_name__ :					Any  			=  middle - 1

		return False





def lowerCamelCase    (    ):





		"""simple docstring"""







		__magic_name__ :					Union[str, Any]  			=  [n for n in range(1001	,	1_0000	,	2	) if is_prime(lowerCamelCase__	)]
		__magic_name__ :					List[Any]  			=  []

		for number in prime_list:
				__magic_name__ :					str  			=  []

				for prime_member in permutations(list(str(lowerCamelCase__	)	)	):
						__magic_name__ :					List[Any]  			=  int(''.join(lowerCamelCase__	)	)

						if prime % 2 == 0:
								continue

						if search(lowerCamelCase__	,	lowerCamelCase__	):
								tmp_numbers.append(lowerCamelCase__	)

				tmp_numbers.sort()
				if len(lowerCamelCase__	) >= 3:
						candidates.append(lowerCamelCase__	)

		__magic_name__ :					Optional[Any]  			=  []
		for candidate in candidates:
				__magic_name__ :					List[str]  			=  len(lowerCamelCase__	)
				__magic_name__ :					List[str]  			=  False

				for i in range(lowerCamelCase__	):
						for j in range(i + 1	,	lowerCamelCase__	):
								for k in range(j + 1	,	lowerCamelCase__	):
										if (
										    abs(candidate[i] - candidate[j]	)
										    == abs(candidate[j] - candidate[k]	)
										    and len({candidate[i], candidate[j], candidate[k]}	) == 3
										):
												passed.append(
												    sorted([candidate[i], candidate[j], candidate[k]]	)	)
												__magic_name__ :					str  			=  True

										if found:
												break
								if found:
										break
						if found:
								break

		__magic_name__ :					Union[str, Any]  			=  set()
		for seq in passed:
				answer.add(''.join([str(lowerCamelCase__	) for i in seq]	)	)

		return max(int(lowerCamelCase__	) for x in answer	)


if __name__ == "__main__":
							print(solution())



'''simple docstring'''

import os
import pickle
import tempfile
import unittest
from typing import Callable, Optional

import numpy as np

from transformers import (
    BatchEncoding,
    BertTokenizer,
    BertTokenizerFast,
    PreTrainedTokenizer,
    PreTrainedTokenizerFast,
    TensorType,
    TokenSpan,
    is_tokenizers_available,
)
from transformers.models.gpta.tokenization_gpta import GPTaTokenizer
from transformers.testing_utils import CaptureStderr, require_flax, require_tf, require_tokenizers, require_torch, slow


if is_tokenizers_available():
							from tokenizers import Tokenizer
							from tokenizers.models import WordPiece
class _lowerCamelCase (		unittest.TestCase							):



		'''simple docstring'''







		def      __lowerCAmelCase	(      self	:		Any						,  _A	:		Optional[Any]    )						->				Optional[int]:
			__magic_name__ :					Optional[int]  			=  list(tokenizer_class.max_model_input_sizes.keys()    )
			for model_name in sa_models[:1]:
				__magic_name__ :					List[str]  			=  tokenizer_class.from_pretrained(_A    )
				self.assertIsNotNone(_A    )
				self.assertIsInstance(_A						,  _A    )
				self.assertIsInstance(_A						,  _A    )

				for special_tok in tokenizer.all_special_tokens:
					self.assertIsInstance(_A						,  _A    )
					__magic_name__ :					Optional[Any]  			=  tokenizer.convert_tokens_to_ids(_A    )
					self.assertIsInstance(_A						,  _A    )







		def      __lowerCAmelCase	(      self	:		Optional[Any]						,  _A	:		BatchEncoding						,  _A	:		Optional[Callable] = None    )						->				Tuple:
			__magic_name__ :					Union[str, Any]  			=  pickle.dumps(_A    )
			self.assertIsNotNone(_A    )

			__magic_name__ :					Optional[Any]  			=  pickle.loads(_A    )

			# Ensure is_fast is correctly restored
			self.assertEqual(be_restored.is_fast						,  be_original.is_fast    )

			# Ensure encodings are potentially correctly restored
			if be_original.is_fast:
				self.assertIsNotNone(be_restored.encodings    )
			else:
				self.assertIsNone(be_restored.encodings    )

			# Ensure the keys are the same
			for original_v, restored_v in zip(be_original.values()						,  be_restored.values()    ):
				if equal_op:
					self.assertTrue(equal_op(_A						,  _A    )    )
				else:
					self.assertEqual(_A						,  _A    )







		@slow
		def      __lowerCAmelCase	(      self	:		Dict    )						->				Optional[Any]:
			self.check_tokenizer_from_pretrained(_A    )







		def      __lowerCAmelCase	(      self	:		str    )						->				List[Any]:
			self.assertEqual(TensorType('tf'    )						,  TensorType.TENSORFLOW    )
			self.assertEqual(TensorType('pt'    )						,  TensorType.PYTORCH    )
			self.assertEqual(TensorType('np'    )						,  TensorType.NUMPY    )







		@require_tokenizers
		def      __lowerCAmelCase	(      self	:		List[str]    )						->				Optional[int]:
			import numpy as np

			__magic_name__ :					Dict  			=  BertTokenizer.from_pretrained('bert-base-cased'    )
			__magic_name__ :					str  			=  BertTokenizerFast.from_pretrained('bert-base-cased'    )

			# Python no tensor
			with self.subTest('BatchEncoding (Python, return_tensors=None)'    ):
				self.assert_dump_and_restore(tokenizer_p('Small example to encode'    )    )

			with self.subTest('BatchEncoding (Python, return_tensors=NUMPY)'    ):
				self.assert_dump_and_restore(
				    tokenizer_p('Small example to encode'						,  return_tensors=TensorType.NUMPY    )						,  np.array_equal    )

			with self.subTest('BatchEncoding (Rust, return_tensors=None)'    ):
				self.assert_dump_and_restore(tokenizer_r('Small example to encode'    )    )

			with self.subTest('BatchEncoding (Rust, return_tensors=NUMPY)'    ):
				self.assert_dump_and_restore(
				    tokenizer_r('Small example to encode'						,  return_tensors=TensorType.NUMPY    )						,  np.array_equal    )







		@require_tf
		@require_tokenizers
		def      __lowerCAmelCase	(      self	:		List[Any]    )						->				List[str]:
			import tensorflow as tf

			def tf_array_equals(_A	:		str						,  _A	:		Union[str, Any]    ):
				return tf.reduce_all(tf.equal(_A						,  _A    )    )

			__magic_name__ :					str  			=  BertTokenizer.from_pretrained('bert-base-cased'    )
			__magic_name__ :					Optional[Any]  			=  BertTokenizerFast.from_pretrained('bert-base-cased'    )

			with self.subTest('BatchEncoding (Python, return_tensors=TENSORFLOW)'    ):
				self.assert_dump_and_restore(
				    tokenizer_p('Small example to encode'						,  return_tensors=TensorType.TENSORFLOW    )						,  _A    )

			with self.subTest('BatchEncoding (Rust, return_tensors=TENSORFLOW)'    ):
				self.assert_dump_and_restore(
				    tokenizer_r('Small example to encode'						,  return_tensors=TensorType.TENSORFLOW    )						,  _A    )







		@require_torch
		@require_tokenizers
		def      __lowerCAmelCase	(      self	:		Any    )						->				List[str]:
			import torch

			__magic_name__ :					Union[str, Any]  			=  BertTokenizer.from_pretrained('bert-base-cased'    )
			__magic_name__ :					Optional[int]  			=  BertTokenizerFast.from_pretrained('bert-base-cased'    )

			with self.subTest('BatchEncoding (Python, return_tensors=PYTORCH)'    ):
				self.assert_dump_and_restore(
				    tokenizer_p('Small example to encode'						,  return_tensors=TensorType.PYTORCH    )						,  torch.equal    )

			with self.subTest('BatchEncoding (Rust, return_tensors=PYTORCH)'    ):
				self.assert_dump_and_restore(
				    tokenizer_r('Small example to encode'						,  return_tensors=TensorType.PYTORCH    )						,  torch.equal    )







		@require_tokenizers
		def      __lowerCAmelCase	(      self	:		List[str]    )						->				Dict:
			__magic_name__ :					Optional[int]  			=  BertTokenizer.from_pretrained('bert-base-cased'    )
			__magic_name__ :					Dict  			=  BertTokenizerFast.from_pretrained('bert-base-cased'    )

			with self.subTest('Python Tokenizer'    ):
				self.assertFalse(tokenizer_p('Small example to_encode'    ).is_fast    )

			with self.subTest('Rust Tokenizer'    ):
				self.assertTrue(tokenizer_r('Small example to_encode'    ).is_fast    )







		@require_tokenizers
		def      __lowerCAmelCase	(      self	:		Union[str, Any]    )						->				Optional[int]:
			__magic_name__ :					Optional[int]  			=  BertTokenizerFast.from_pretrained('bert-base-cased'    )
			__magic_name__ :					Tuple  			=  tokenizer_r(['Test', '\xad', 'test']						,  is_split_into_words=_A    )

			self.assertEqual(encoded.word_to_tokens(0    )						,  TokenSpan(start=1						,  end=2    )    )
			self.assertEqual(encoded.word_to_tokens(1    )						,  _A    )
			self.assertEqual(encoded.word_to_tokens(2    )						,  TokenSpan(start=2						,  end=3    )    )







		def      __lowerCAmelCase	(      self	:		Optional[int]    )						->				Optional[Any]:
			__magic_name__ :					Any  			=  BatchEncoding({'inputs': [[1, 2, 3], [4, 5, 6]], 'labels': [0, 1]}    )
			__magic_name__ :					Dict  			=  batch.convert_to_tensors(tensor_type='np'    )
			self.assertEqual(tensor_batch['inputs'].shape						,  (2, 3)    )
			self.assertEqual(tensor_batch['labels'].shape						,  (2,)    )
			# test converting the converted
			with CaptureStderr() as cs:
				__magic_name__ :					Any  			=  batch.convert_to_tensors(tensor_type='np'    )
			self.assertFalse(len(cs.err    )						,  msg=F'should have no warning, but got {cs.err}'    )

			__magic_name__ :					Optional[Any]  			=  BatchEncoding({'inputs': [1, 2, 3], 'labels': 0}    )
			__magic_name__ :					List[Any]  			=  batch.convert_to_tensors(tensor_type='np'						,  prepend_batch_axis=_A    )
			self.assertEqual(tensor_batch['inputs'].shape						,  (1, 3)    )
			self.assertEqual(tensor_batch['labels'].shape						,  (1,)    )







		@require_torch
		def      __lowerCAmelCase	(      self	:		Union[str, Any]    )						->				Any:
			__magic_name__ :					Optional[int]  			=  BatchEncoding({'inputs': [[1, 2, 3], [4, 5, 6]], 'labels': [0, 1]}    )
			__magic_name__ :					List[Any]  			=  batch.convert_to_tensors(tensor_type='pt'    )
			self.assertEqual(tensor_batch['inputs'].shape						,  (2, 3)    )
			self.assertEqual(tensor_batch['labels'].shape						,  (2,)    )
			# test converting the converted
			with CaptureStderr() as cs:
				__magic_name__ :					Union[str, Any]  			=  batch.convert_to_tensors(tensor_type='pt'    )
			self.assertFalse(len(cs.err    )						,  msg=F'should have no warning, but got {cs.err}'    )

			__magic_name__ :					Any  			=  BatchEncoding({'inputs': [1, 2, 3], 'labels': 0}    )
			__magic_name__ :					str  			=  batch.convert_to_tensors(tensor_type='pt'						,  prepend_batch_axis=_A    )
			self.assertEqual(tensor_batch['inputs'].shape						,  (1, 3)    )
			self.assertEqual(tensor_batch['labels'].shape						,  (1,)    )







		@require_tf
		def      __lowerCAmelCase	(      self	:		Optional[Any]    )						->				List[str]:
			__magic_name__ :					str  			=  BatchEncoding({'inputs': [[1, 2, 3], [4, 5, 6]], 'labels': [0, 1]}    )
			__magic_name__ :					List[str]  			=  batch.convert_to_tensors(tensor_type='tf'    )
			self.assertEqual(tensor_batch['inputs'].shape						,  (2, 3)    )
			self.assertEqual(tensor_batch['labels'].shape						,  (2,)    )
			# test converting the converted
			with CaptureStderr() as cs:
				__magic_name__ :					Optional[int]  			=  batch.convert_to_tensors(tensor_type='tf'    )
			self.assertFalse(len(cs.err    )						,  msg=F'should have no warning, but got {cs.err}'    )

			__magic_name__ :					Union[str, Any]  			=  BatchEncoding({'inputs': [1, 2, 3], 'labels': 0}    )
			__magic_name__ :					Union[str, Any]  			=  batch.convert_to_tensors(tensor_type='tf'						,  prepend_batch_axis=_A    )
			self.assertEqual(tensor_batch['inputs'].shape						,  (1, 3)    )
			self.assertEqual(tensor_batch['labels'].shape						,  (1,)    )







		@require_flax
		def      __lowerCAmelCase	(      self	:		str    )						->				Optional[Any]:
			__magic_name__ :					List[Any]  			=  BatchEncoding({'inputs': [[1, 2, 3], [4, 5, 6]], 'labels': [0, 1]}    )
			__magic_name__ :					int  			=  batch.convert_to_tensors(tensor_type='jax'    )
			self.assertEqual(tensor_batch['inputs'].shape						,  (2, 3)    )
			self.assertEqual(tensor_batch['labels'].shape						,  (2,)    )
			# test converting the converted
			with CaptureStderr() as cs:
				__magic_name__ :					Optional[Any]  			=  batch.convert_to_tensors(tensor_type='jax'    )
			self.assertFalse(len(cs.err    )						,  msg=F'should have no warning, but got {cs.err}'    )

			__magic_name__ :					str  			=  BatchEncoding({'inputs': [1, 2, 3], 'labels': 0}    )
			__magic_name__ :					Dict  			=  batch.convert_to_tensors(tensor_type='jax'						,  prepend_batch_axis=_A    )
			self.assertEqual(tensor_batch['inputs'].shape						,  (1, 3)    )
			self.assertEqual(tensor_batch['labels'].shape						,  (1,)    )







		def      __lowerCAmelCase	(      self	:		str    )						->				int:
			__magic_name__ :					int  			=  [{'input_ids': np.array([0, 1, 2]    )}, {'input_ids': np.array([0, 1, 2, 3]    )}]
			__magic_name__ :					Dict  			=  BertTokenizer.from_pretrained('bert-base-cased'    )

			__magic_name__ :					Optional[int]  			=  tokenizer.pad(_A						,  padding=_A    )
			self.assertTrue(isinstance(batch['input_ids']						,  np.ndarray    )    )
			self.assertEqual(batch['input_ids'].tolist()						,  [[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )
			__magic_name__ :					Dict  			=  tokenizer.pad(_A						,  padding=_A						,  return_tensors='np'    )
			self.assertTrue(isinstance(batch['input_ids']						,  np.ndarray    )    )
			self.assertEqual(batch['input_ids'].tolist()						,  [[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )







		@require_torch
		def      __lowerCAmelCase	(      self	:		List[Any]    )						->				str:
			import torch

			__magic_name__ :					List[str]  			=  [{'input_ids': torch.tensor([0, 1, 2]    )}, {'input_ids': torch.tensor([0, 1, 2, 3]    )}]
			__magic_name__ :					List[str]  			=  BertTokenizer.from_pretrained('bert-base-cased'    )

			__magic_name__ :					List[Any]  			=  tokenizer.pad(_A						,  padding=_A    )
			self.assertTrue(isinstance(batch['input_ids']						,  torch.Tensor    )    )
			self.assertEqual(batch['input_ids'].tolist()						,  [[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )
			__magic_name__ :					Union[str, Any]  			=  tokenizer.pad(_A						,  padding=_A						,  return_tensors='pt'    )
			self.assertTrue(isinstance(batch['input_ids']						,  torch.Tensor    )    )
			self.assertEqual(batch['input_ids'].tolist()						,  [[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )







		@require_tf
		def      __lowerCAmelCase	(      self	:		Any    )						->				Optional[int]:
			import tensorflow as tf

			__magic_name__ :					Tuple  			=  [{'input_ids': tf.constant([0, 1, 2]    )}, {'input_ids': tf.constant([0, 1, 2, 3]    )}]
			__magic_name__ :					Any  			=  BertTokenizer.from_pretrained('bert-base-cased'    )

			__magic_name__ :					Any  			=  tokenizer.pad(_A						,  padding=_A    )
			self.assertTrue(isinstance(batch['input_ids']						,  tf.Tensor    )    )
			self.assertEqual(batch['input_ids'].numpy().tolist()						,  [[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )
			__magic_name__ :					Union[str, Any]  			=  tokenizer.pad(_A						,  padding=_A						,  return_tensors='tf'    )
			self.assertTrue(isinstance(batch['input_ids']						,  tf.Tensor    )    )
			self.assertEqual(batch['input_ids'].numpy().tolist()						,  [[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )







		@require_tokenizers
		def      __lowerCAmelCase	(      self	:		Any    )						->				str:
			__magic_name__ :					str  			=  Tokenizer(WordPiece(unk_token='[UNK]'    )    )
			PreTrainedTokenizerFast(tokenizer_object=_A    )







		@require_tokenizers
		def      __lowerCAmelCase	(      self	:		Dict    )						->				Any:
			__magic_name__ :					List[Any]  			=  Tokenizer(WordPiece(unk_token='[UNK]'    )    )
			with tempfile.TemporaryDirectory() as tmpdirname:
				bert_tokenizer.save(os.path.join(_A						,  'tokenizer.json'    )    )
				PreTrainedTokenizerFast(tokenizer_file=os.path.join(_A						,  'tokenizer.json'    )    )