


def       _lowerCAmelCase    (				lowerCAmelCase_				:int = 100				)->int:
   '''simple docstring'''






   snake_case_            =       n * (n + 1) * (2 * n + 1) / 6
   snake_case_            =       (n * (n + 1) / 2) ** 2
   return int(square_of_sum - sum_of_squares				)


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








'''simple docstring'''



import inspect
import unittest

import numpy as np

from transformers import ViTConfig, is_flax_available
from transformers.testing_utils import require_flax, slow

from ...test_configuration_common import ConfigTester
from ...test_modeling_flax_common import FlaxModelTesterMixin, floats_tensor


if is_flax_available():
      import jax

      from transformers.models.vit.modeling_flax_vit import FlaxViTForImageClassification, FlaxViTModel





class   UpperCAmelCase_    (unittest.TestCase    ):





    """simple docstring"""






    def __init__(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_=13     ,	SCREAMING_SNAKE_CASE_=30     ,	SCREAMING_SNAKE_CASE_=2     ,	SCREAMING_SNAKE_CASE_=3     ,	SCREAMING_SNAKE_CASE_=True     ,	SCREAMING_SNAKE_CASE_=True     ,	SCREAMING_SNAKE_CASE_=32     ,	SCREAMING_SNAKE_CASE_=5     ,	SCREAMING_SNAKE_CASE_=4     ,	SCREAMING_SNAKE_CASE_=37     ,	SCREAMING_SNAKE_CASE_="gelu"     ,	SCREAMING_SNAKE_CASE_=0.1     ,	SCREAMING_SNAKE_CASE_=0.1     ,	SCREAMING_SNAKE_CASE_=10     ,	SCREAMING_SNAKE_CASE_=0.0_2     ,	)							->	Optional[int]:
         __lowerCamelCase  :      Optional[int]														=						parent
         __lowerCamelCase  :      Dict														=						batch_size
         __lowerCamelCase  :      int														=						image_size
         __lowerCamelCase  :      List[str]														=						patch_size
         __lowerCamelCase  :      Optional[int]														=						num_channels
         __lowerCamelCase  :      Any														=						is_training
         __lowerCamelCase  :      Dict														=						use_labels
         __lowerCamelCase  :      List[Any]														=						hidden_size
         __lowerCamelCase  :      List[Any]														=						num_hidden_layers
         __lowerCamelCase  :      Optional[Any]														=						num_attention_heads
         __lowerCamelCase  :      Dict														=						intermediate_size
         __lowerCamelCase  :      Union[str, Any]														=						hidden_act
         __lowerCamelCase  :      Optional[int]														=						hidden_dropout_prob
         __lowerCamelCase  :      Tuple														=						attention_probs_dropout_prob
         __lowerCamelCase  :      str														=						type_sequence_label_size
         __lowerCamelCase  :      List[str]														=						initializer_range

         # in ViT, the seq length equals the number of patches + 1 (we add 1 for the [CLS] token)
         __lowerCamelCase  :      str														=						(image_size // patch_size) ** 2
         __lowerCamelCase  :      Optional[int]														=						num_patches + 1







    def  lowercase_							(				self      )							->	Union[str, Any]:
         __lowerCamelCase  :      int														=						floats_tensor([self.batch_size, self.num_channels, self.image_size, self.image_size]      )

         __lowerCamelCase  :      Optional[int]														=						ViTConfig(
             image_size=self.image_size     ,	patch_size=self.patch_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     ,	is_decoder=SCREAMING_SNAKE_CASE_     ,	initializer_range=self.initializer_range     ,	)

         return config, pixel_values







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )							->	Union[str, Any]:
         __lowerCamelCase  :      Union[str, Any]														=						FlaxViTModel(config=SCREAMING_SNAKE_CASE_      )
         __lowerCamelCase  :      str														=						model(SCREAMING_SNAKE_CASE_      )
         # expected sequence length = num_patches + 1 (we add 1 for the [CLS] token)
         __lowerCamelCase  :      str														=						(self.image_size, self.image_size)
         __lowerCamelCase  :      str														=						(self.patch_size, self.patch_size)
         __lowerCamelCase  :      Any														=						(image_size[1] // patch_size[1]) * (image_size[0] // patch_size[0])
         self.parent.assertEqual(result.last_hidden_state.shape     ,	(self.batch_size, num_patches + 1, self.hidden_size)      )







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )							->	str:
         __lowerCamelCase  :      Tuple														=						self.type_sequence_label_size
         __lowerCamelCase  :      Any														=						FlaxViTForImageClassification(config=SCREAMING_SNAKE_CASE_      )
         __lowerCamelCase  :      Dict														=						model(SCREAMING_SNAKE_CASE_      )
         self.parent.assertEqual(result.logits.shape     ,	(self.batch_size, self.type_sequence_label_size)      )

         # test greyscale images
         __lowerCamelCase  :      List[str]														=						1
         __lowerCamelCase  :      List[Any]														=						FlaxViTForImageClassification(SCREAMING_SNAKE_CASE_      )

         __lowerCamelCase  :      str														=						floats_tensor([self.batch_size, 1, self.image_size, self.image_size]      )
         __lowerCamelCase  :      List[Any]														=						model(SCREAMING_SNAKE_CASE_      )







    def  lowercase_							(				self      )							->	Optional[int]:
         __lowerCamelCase  :      List[Any]														=						self.prepare_config_and_inputs()
         (
             (
             __lowerCamelCase
         )							,			(
             __lowerCamelCase
         )							,			
         )  :      int														=						config_and_inputs
         __lowerCamelCase  :      Union[str, Any]														=						{'pixel_values': pixel_values}
         return config, inputs_dict







@require_flax
class   UpperCAmelCase_    (_UpperCAmelCase   ,						unittest.TestCase    ):





    """simple docstring"""






    lowerCamelCase    :   str					=     (FlaxViTModel, FlaxViTForImageClassification) if is_flax_available() else ()







    def  lowercase_							(				self      )							->	None:
         __lowerCamelCase  :      str														=						FlaxViTModelTester(self      )
         __lowerCamelCase  :      Union[str, Any]														=						ConfigTester(self     ,	config_class=SCREAMING_SNAKE_CASE_     ,	has_text_modality=SCREAMING_SNAKE_CASE_     ,	hidden_size=37      )







    def  lowercase_							(				self      )							->	List[Any]:
         self.config_tester.run_common_tests()







    def  lowercase_							(				self      )							->	Optional[Any]:
         __lowerCamelCase  :      Optional[int]														=						self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_model(*SCREAMING_SNAKE_CASE_      )







    def  lowercase_							(				self      )							->	Any:
         __lowerCamelCase  :      List[Any]														=						self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_for_image_classification(*SCREAMING_SNAKE_CASE_      )







    def  lowercase_							(				self      )							->	Optional[Any]:
         __lowerCamelCase							,			__lowerCamelCase  :      Optional[int]														=						self.model_tester.prepare_config_and_inputs_for_common()

         for model_class in self.all_model_classes:
              __lowerCamelCase  :      Optional[Any]														=						model_class(SCREAMING_SNAKE_CASE_      )
              __lowerCamelCase  :      Dict														=						inspect.signature(model.__call__      )
              # signature.parameters is an OrderedDict => so arg_names order is deterministic
              __lowerCamelCase  :      List[str]														=						[*signature.parameters.keys()]

              __lowerCamelCase  :      Optional[int]														=						['pixel_values']
              self.assertListEqual(arg_names[:1]     ,	SCREAMING_SNAKE_CASE_      )







    def  lowercase_							(				self      )							->	Any:
         __lowerCamelCase							,			__lowerCamelCase  :      Dict														=						self.model_tester.prepare_config_and_inputs_for_common()

         for model_class in self.all_model_classes:
              with self.subTest(model_class.__name__      ):
                   __lowerCamelCase  :      List[Any]														=						self._prepare_for_class(SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )
                   __lowerCamelCase  :      Optional[int]														=						model_class(SCREAMING_SNAKE_CASE_      )

                   @jax.jit
                   def model_jitted(SCREAMING_SNAKE_CASE_     ,	**SCREAMING_SNAKE_CASE_      ):
                        return model(pixel_values=SCREAMING_SNAKE_CASE_     ,	**SCREAMING_SNAKE_CASE_      )

                   with self.subTest('JIT Enabled'      ):
                        __lowerCamelCase  :      Optional[int]														=						model_jitted(**SCREAMING_SNAKE_CASE_      ).to_tuple()

                   with self.subTest('JIT Disabled'      ):
                        with jax.disable_jit():
                             __lowerCamelCase  :      Union[str, Any]														=						model_jitted(**SCREAMING_SNAKE_CASE_      ).to_tuple()

                   self.assertEqual(len(SCREAMING_SNAKE_CASE_      )     ,	len(SCREAMING_SNAKE_CASE_      )      )
                   for jitted_output, output in zip(SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      ):
                        self.assertEqual(jitted_output.shape     ,	output.shape      )







    @slow
    def  lowercase_							(				self      )							->	List[Any]:
         for model_class_name in self.all_model_classes:
              __lowerCamelCase  :      Union[str, Any]														=						model_class_name.from_pretrained('google/vit-base-patch16-224'      )
              __lowerCamelCase  :      Union[str, Any]														=						model(np.ones((1, 3, 2_24, 2_24)      )      )
              self.assertIsNotNone(SCREAMING_SNAKE_CASE_      )






