


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 copy
import inspect
import unittest

import numpy as np
from huggingface_hub import hf_hub_download

from transformers import VivitConfig
from transformers.models.auto import get_values
from transformers.testing_utils import require_torch, require_vision, slow, torch_device
from transformers.utils import cached_property, is_torch_available, is_vision_available

from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, floats_tensor, ids_tensor


if is_torch_available():
							import torch
							from torch import nn

							from transformers import MODEL_FOR_VIDEO_CLASSIFICATION_MAPPING, VivitForVideoClassification, VivitModel
							from transformers.models.vivit.modeling_vivit import VIVIT_PRETRAINED_MODEL_ARCHIVE_LIST


if is_vision_available():
							from transformers import VivitImageProcessor

class   A__							:




						def __init__(				self    :					str ,			_a    :					List[str] ,			_a    :					List[str]=2 ,			_a    :					Dict=True ,			_a    :					Tuple=True ,			_a    :					Any=10 ,			_a    :					str=10 ,			_a    :					int=8 ,			_a    :					Tuple=[2, 4, 4] ,			_a    :					Optional[int]=3 ,			_a    :					List[str]=768 ,			_a    :					int=5 ,			_a    :					Any=4 ,			_a    :					Tuple=37 ,			_a    :					Tuple="gelu_fast" ,			_a    :					Dict=0.0 ,			_a    :					Optional[Any]=0.0 ,			_a    :					Optional[Any]=0.02 ,			_a    :					str=1E-06 ,			_a    :					Tuple=True ,			_a    :					List[str]=None ,			)							->   Dict:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =parent
										_SCREAMING_SNAKE_CASE	     =batch_size
										_SCREAMING_SNAKE_CASE	     =is_training
										_SCREAMING_SNAKE_CASE	     =use_labels
										_SCREAMING_SNAKE_CASE	     =num_labels
										_SCREAMING_SNAKE_CASE	     =image_size
										_SCREAMING_SNAKE_CASE	     =num_frames
										_SCREAMING_SNAKE_CASE	     =tubelet_size
										_SCREAMING_SNAKE_CASE	     =num_channels
										_SCREAMING_SNAKE_CASE	     =hidden_size
										_SCREAMING_SNAKE_CASE	     =num_hidden_layers
										_SCREAMING_SNAKE_CASE	     =num_attention_heads
										_SCREAMING_SNAKE_CASE	     =intermediate_size
										_SCREAMING_SNAKE_CASE	     =hidden_act
										_SCREAMING_SNAKE_CASE	     =hidden_dropout_prob
										_SCREAMING_SNAKE_CASE	     =attention_probs_dropout_prob
										_SCREAMING_SNAKE_CASE	     =initializer_range
										_SCREAMING_SNAKE_CASE	     =layer_norm_eps
										_SCREAMING_SNAKE_CASE	     =qkv_bias
										_SCREAMING_SNAKE_CASE	     =scope

										_SCREAMING_SNAKE_CASE	     =(
										    (self.image_size // self.tubelet_size[2])
										    * (self.image_size // self.tubelet_size[1])
										    * (self.num_frames // self.tubelet_size[0])
										) + 1  # CLS token




						def 							__UpperCamelCase (				self    :					List[str]     )							->   str:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =floats_tensor(
										    [self.batch_size, self.num_frames, self.num_channels, self.image_size, self.image_size]     )

										_SCREAMING_SNAKE_CASE	     =None
										if self.use_labels:
														_SCREAMING_SNAKE_CASE	     =ids_tensor([self.batch_size] ,			self.num_labels     )

										_SCREAMING_SNAKE_CASE	     =self.get_config()

										return config, pixel_values, labels




						def 							__UpperCamelCase (				self    :					Optional[int]     )							->   List[Any]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =VivitConfig(
										    num_frames=self.num_frames ,			image_size=self.image_size ,			tubelet_size=self.tubelet_size ,			num_channels=self.num_channels ,			hidden_size=self.hidden_size ,			num_hidden_layers=self.num_hidden_layers ,			num_attention_heads=self.num_attention_heads ,			intermediate_size=self.intermediate_size ,			hidden_act=self.hidden_act ,			hidden_dropout_prob=self.hidden_dropout_prob ,			attention_probs_dropout_prob=self.attention_probs_dropout_prob ,			initializer_range=self.initializer_range ,			layer_norm_eps=self.layer_norm_eps ,			qkv_bias=self.qkv_bias ,			)
										_SCREAMING_SNAKE_CASE	     =self.num_labels
										return config




						def 							__UpperCamelCase (				self    :					Union[str, Any] ,			_a    :					Optional[int] ,			_a    :					Dict ,			_a    :					Tuple     )							->   Union[str, Any]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =VivitModel(config=_a     )
										model.to(_a     )
										model.eval()
										_SCREAMING_SNAKE_CASE	     =model(_a     )
										self.parent.assertEqual(result.last_hidden_state.shape ,			(self.batch_size, self.seq_length, self.hidden_size)     )




						def 							__UpperCamelCase (				self    :					Union[str, Any] ,			_a    :					Optional[Any] ,			_a    :					Any ,			_a    :					Any     )							->   int:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =VivitForVideoClassification(_a     )
										model.to(_a     )
										model.eval()

										_SCREAMING_SNAKE_CASE	     =model(_a     )

										# verify the logits shape
										_SCREAMING_SNAKE_CASE	     =torch.Size((self.batch_size, self.num_labels)     )
										self.parent.assertEqual(result.logits.shape ,			_a     )




						def 							__UpperCamelCase (				self    :					Tuple     )							->   List[str]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =self.prepare_config_and_inputs()
										_SCREAMING_SNAKE_CASE     , _SCREAMING_SNAKE_CASE     , _SCREAMING_SNAKE_CASE	     =config_and_inputs
										_SCREAMING_SNAKE_CASE	     ={'''pixel_values''': pixel_values}
										return config, inputs_dict

@require_torch
class   A__							(						UpperCamelCase__      ,   unittest.TestCase     ):
						UpperCAmelCase									=  (VivitModel, VivitForVideoClassification) if is_torch_available() else ()

						UpperCAmelCase									=  False
						UpperCAmelCase									=  False
						UpperCAmelCase									=  False
						UpperCAmelCase									=  False




						def 							__UpperCamelCase (				self    :					Any     )							->   Any:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =VivitModelTester(self     )
										_SCREAMING_SNAKE_CASE	     =ConfigTester(self ,			config_class=_a ,			has_text_modality=_a ,			hidden_size=37     )




						def 							__UpperCamelCase (				self    :					List[str] ,			_a    :					List[str] ,			_a    :					Union[str, Any] ,			_a    :					Dict=False     )							->   List[str]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =copy.deepcopy(_a     )

										if return_labels:
														if model_class in get_values(_a     ):
																		_SCREAMING_SNAKE_CASE	     =torch.zeros(
																		    self.model_tester.batch_size ,			dtype=torch.long ,			device=_a     )

										return inputs_dict




						def 							__UpperCamelCase (				self    :					str     )							->   Optional[int]:


										"""simple docstring"""





										self.config_tester.run_common_tests()




						@unittest.skip(reason='''Vivit does not use inputs_embeds'''     )
						def 							__UpperCamelCase (				self    :					Optional[Any]     )							->   Any:


										"""simple docstring"""





										pass




						def 							__UpperCamelCase (				self    :					str     )							->   Dict:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE     , _SCREAMING_SNAKE_CASE	     =self.model_tester.prepare_config_and_inputs_for_common()

										for model_class in self.all_model_classes:
														_SCREAMING_SNAKE_CASE	     =model_class(_a     )
														self.assertIsInstance(model.get_input_embeddings() ,			(nn.Module)     )
														_SCREAMING_SNAKE_CASE	     =model.get_output_embeddings()
														self.assertTrue(x is None or isinstance(_a ,			nn.Linear     )     )




						def 							__UpperCamelCase (				self    :					int     )							->   str:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE     , _SCREAMING_SNAKE_CASE	     =self.model_tester.prepare_config_and_inputs_for_common()

										for model_class in self.all_model_classes:
														_SCREAMING_SNAKE_CASE	     =model_class(_a     )
														_SCREAMING_SNAKE_CASE	     =inspect.signature(model.forward     )
														# signature.parameters is an OrderedDict => so arg_names order is deterministic
														_SCREAMING_SNAKE_CASE	     =[*signature.parameters.keys()]

														_SCREAMING_SNAKE_CASE	     =['''pixel_values''', '''head_mask''']
														self.assertListEqual(arg_names[:2] ,			_a     )




						def 							__UpperCamelCase (				self    :					Tuple     )							->   List[Any]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =self.model_tester.prepare_config_and_inputs()
										self.model_tester.create_and_check_model(*_a     )




						def 							__UpperCamelCase (				self    :					str     )							->   Union[str, Any]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =self.model_tester.prepare_config_and_inputs()
										self.model_tester.create_and_check_for_video_classification(*_a     )




						@slow
						def 							__UpperCamelCase (				self    :					str     )							->   Optional[Any]:


										"""simple docstring"""





										for model_name in VIVIT_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
														_SCREAMING_SNAKE_CASE	     =VivitModel.from_pretrained(_a     )
														self.assertIsNotNone(_a     )




						def 							__UpperCamelCase (				self    :					List[Any]     )							->   Tuple:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE     , _SCREAMING_SNAKE_CASE	     =self.model_tester.prepare_config_and_inputs_for_common()
										_SCREAMING_SNAKE_CASE	     =True

										for model_class in self.all_model_classes:
														_SCREAMING_SNAKE_CASE	     =self.model_tester.seq_length

														_SCREAMING_SNAKE_CASE	     =True
														_SCREAMING_SNAKE_CASE	     =False
														_SCREAMING_SNAKE_CASE	     =True
														_SCREAMING_SNAKE_CASE	     =model_class(_a     )
														model.to(_a     )
														model.eval()
														with torch.no_grad():
																		_SCREAMING_SNAKE_CASE	     =model(**self._prepare_for_class(_a ,			_a     )     )
														_SCREAMING_SNAKE_CASE	     =outputs.attentions
														self.assertEqual(len(_a     ) ,			self.model_tester.num_hidden_layers     )

														# check that output_attentions also work using config
														del inputs_dict["output_attentions"]
														_SCREAMING_SNAKE_CASE	     =True
														_SCREAMING_SNAKE_CASE	     =model_class(_a     )
														model.to(_a     )
														model.eval()
														with torch.no_grad():
																		_SCREAMING_SNAKE_CASE	     =model(**self._prepare_for_class(_a ,			_a     )     )
														_SCREAMING_SNAKE_CASE	     =outputs.attentions
														self.assertEqual(len(_a     ) ,			self.model_tester.num_hidden_layers     )

														self.assertListEqual(
														    list(attentions[0].shape[-3:]     ) ,			[self.model_tester.num_attention_heads, seq_len, seq_len] ,			)
														_SCREAMING_SNAKE_CASE	     =len(_a     )

														# Check attention is always last and order is fine
														_SCREAMING_SNAKE_CASE	     =True
														_SCREAMING_SNAKE_CASE	     =True
														_SCREAMING_SNAKE_CASE	     =model_class(_a     )
														model.to(_a     )
														model.eval()
														with torch.no_grad():
																		_SCREAMING_SNAKE_CASE	     =model(**self._prepare_for_class(_a ,			_a     )     )

														self.assertEqual(out_len + 1 ,			len(_a     )     )

														_SCREAMING_SNAKE_CASE	     =outputs.attentions

														self.assertEqual(len(_a     ) ,			self.model_tester.num_hidden_layers     )

														self.assertListEqual(
														    list(self_attentions[0].shape[-3:]     ) ,			[self.model_tester.num_attention_heads, seq_len, seq_len] ,			)




						def 							__UpperCamelCase (				self    :					Any     )							->   Optional[int]:


										"""simple docstring"""





										def check_hidden_states_output(_a    :					Dict ,			_a    :					Optional[Any] ,			_a    :					List[Any]     ):
														_SCREAMING_SNAKE_CASE	     =model_class(_a     )
														model.to(_a     )
														model.eval()

														with torch.no_grad():
																		_SCREAMING_SNAKE_CASE	     =model(**self._prepare_for_class(_a ,			_a     )     )

														_SCREAMING_SNAKE_CASE	     =outputs.hidden_states
														_SCREAMING_SNAKE_CASE	     =self.model_tester.num_hidden_layers + 1
														self.assertEqual(len(_a     ) ,			_a     )

														_SCREAMING_SNAKE_CASE	     =self.model_tester.seq_length

														self.assertListEqual(
														    list(hidden_states[0].shape[-2:]     ) ,			[seq_length, self.model_tester.hidden_size] ,			)

										_SCREAMING_SNAKE_CASE     , _SCREAMING_SNAKE_CASE	     =self.model_tester.prepare_config_and_inputs_for_common()

										for model_class in self.all_model_classes:
														_SCREAMING_SNAKE_CASE	     =True
														check_hidden_states_output(_a ,			_a ,			_a     )

														# check that output_hidden_states also work using config
														del inputs_dict["output_hidden_states"]
														_SCREAMING_SNAKE_CASE	     =True

														check_hidden_states_output(_a ,			_a ,			_a     )




						@unittest.skip('''Will be fixed soon by reducing the size of the model used for common tests.'''     )
						def 							__UpperCamelCase (				self    :					Optional[int]     )							->   List[Any]:


										"""simple docstring"""





										pass







def   lowerCamelCase(      ):
				_SCREAMING_SNAKE_CASE	     =hf_hub_download(
				    repo_id='''hf-internal-testing/spaghetti-video'''		,filename='''eating_spaghetti_32_frames.npy'''		,repo_type='''dataset''')
				_SCREAMING_SNAKE_CASE	     =np.load(a__)
				return list(a__)


@require_torch
@require_vision
class   A__							(						unittest.TestCase     ):




						@cached_property
						def 							__UpperCamelCase (				self    :					Union[str, Any]     )							->   List[Any]:


										"""simple docstring"""





										return VivitImageProcessor() if is_vision_available() else None




						@slow
						def 							__UpperCamelCase (				self    :					Optional[Any]     )							->   str:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =VivitForVideoClassification.from_pretrained('''google/vivit-b-16x2-kinetics400'''     ).to(_a     )

										_SCREAMING_SNAKE_CASE	     =self.default_image_processor
										_SCREAMING_SNAKE_CASE	     =prepare_video()
										_SCREAMING_SNAKE_CASE	     =image_processor(_a ,			return_tensors='''pt'''     ).to(_a     )

										# forward pass
										with torch.no_grad():
														_SCREAMING_SNAKE_CASE	     =model(**_a     )

										# verify the logits
										_SCREAMING_SNAKE_CASE	     =torch.Size((1, 400)     )
										self.assertEqual(outputs.logits.shape ,			_a     )

										# taken from original model
										_SCREAMING_SNAKE_CASE	     =torch.tensor([-1.05_43, 2.07_64, -0.21_04, 0.44_39, -0.96_58]     ).to(_a     )

										self.assertTrue(torch.allclose(outputs.logits[0, :5] ,			_a ,			atol=1E-4     )     )