



"""simple docstring"""







from __future__ import annotations

from math import ceil, floor, sqrt

def 				UpperCamelCase_    (    lowerCAmelCase__      :				int = 200_0000						)						->   int:

  """simple docstring"""




  lowerCAmelCase_   :				list[int]								= [0]
  lowerCAmelCase_   :				int

  for idx in range(1    ,   ceil(sqrt(target * 2						) * 1.1						)						):
    triangle_numbers.append(triangle_numbers[-1] + idx						)

  # we want this to be as close as possible to target
  lowerCAmelCase_   :				int								= 0
  # the area corresponding to the grid that gives the product closest to target
  lowerCAmelCase_   :				int								= 0
  # an estimate of b, using the quadratic formula
  lowerCAmelCase_   :				float
  # the largest integer less than b_estimate
  lowerCAmelCase_   :				int
  # the largest integer less than b_estimate
  lowerCAmelCase_   :				int
  # the triangle number corresponding to b_floor
  lowerCAmelCase_   :				int
  # the triangle number corresponding to b_ceil
  lowerCAmelCase_   :				int

  for idx_a, triangle_a in enumerate(triangle_numbers[1:]    ,   1						):
    lowerCAmelCase_   :				Union[str, Any]								= (-1 + sqrt(1 + 8 * target / triangle_a						)) / 2
    lowerCAmelCase_   :				str								= floor(lowerCAmelCase__						)
    lowerCAmelCase_   :				Union[str, Any]								= ceil(lowerCAmelCase__						)
    lowerCAmelCase_   :				str								= triangle_numbers[b_floor]
    lowerCAmelCase_   :				Dict								= triangle_numbers[b_ceil]

    if abs(target - triangle_b_first_guess * triangle_a						) < abs(
        target - best_product						):
      lowerCAmelCase_   :				Tuple								= triangle_b_first_guess * triangle_a
      lowerCAmelCase_   :				List[Any]								= idx_a * b_floor

    if abs(target - triangle_b_second_guess * triangle_a						) < abs(
        target - best_product						):
      lowerCAmelCase_   :				List[Any]								= triangle_b_second_guess * triangle_a
      lowerCAmelCase_   :				Optional[int]								= idx_a * b_ceil

  return area


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










"""simple docstring"""







from __future__ import annotations

import inspect
import unittest
from typing import List, Tuple

from transformers import RegNetConfig
from transformers.testing_utils import require_tf, require_vision, slow
from transformers.utils import cached_property, is_tf_available, is_vision_available

from ...test_configuration_common import ConfigTester
from ...test_modeling_tf_common import TFModelTesterMixin, floats_tensor, ids_tensor
from ...test_pipeline_mixin import PipelineTesterMixin


if is_tf_available():
     import tensorflow as tf

     from transformers import TF_REGNET_PRETRAINED_MODEL_ARCHIVE_LIST, TFRegNetForImageClassification, TFRegNetModel


if is_vision_available():
     from PIL import Image

     from transformers import AutoImageProcessor







class       UpperCamelCase__   :




      """simple docstring"""




      def __init__(      self				:      Dict    ,			SCREAMING_SNAKE_CASE_				:      str    ,			SCREAMING_SNAKE_CASE_				:      Optional[Any]=3    ,			SCREAMING_SNAKE_CASE_				:      Any=3_2    ,			SCREAMING_SNAKE_CASE_				:      int=3    ,			SCREAMING_SNAKE_CASE_				:      Optional[Any]=1_0    ,			SCREAMING_SNAKE_CASE_				:      Dict=[1_0, 2_0, 3_0, 4_0]    ,			SCREAMING_SNAKE_CASE_				:      int=[1, 1, 2, 1]    ,			SCREAMING_SNAKE_CASE_				:      int=True    ,			SCREAMING_SNAKE_CASE_				:      Optional[Any]=True    ,			SCREAMING_SNAKE_CASE_				:      int="relu"    ,			SCREAMING_SNAKE_CASE_				:      Union[str, Any]=3    ,			SCREAMING_SNAKE_CASE_				:      List[str]=None    ,			):
        lowerCAmelCase_   :				Optional[int]								= parent
        lowerCAmelCase_   :				Union[str, Any]								= batch_size
        lowerCAmelCase_   :				Optional[int]								= image_size
        lowerCAmelCase_   :				Optional[int]								= num_channels
        lowerCAmelCase_   :				Any								= embeddings_size
        lowerCAmelCase_   :				Dict								= hidden_sizes
        lowerCAmelCase_   :				Any								= depths
        lowerCAmelCase_   :				Optional[int]								= is_training
        lowerCAmelCase_   :				int								= use_labels
        lowerCAmelCase_   :				List[Any]								= hidden_act
        lowerCAmelCase_   :				Dict								= num_labels
        lowerCAmelCase_   :				Optional[int]								= scope
        lowerCAmelCase_   :				Tuple								= len(SCREAMING_SNAKE_CASE_       )



      def      SCREAMING_SNAKE_CASE__ (      self				:      Any       ):
        lowerCAmelCase_   :				List[str]								= floats_tensor([self.batch_size, self.num_channels, self.image_size, self.image_size]       )

        lowerCAmelCase_   :				Union[str, Any]								= None
        if self.use_labels:
          lowerCAmelCase_   :				int								= ids_tensor([self.batch_size]    ,			self.num_labels       )

        lowerCAmelCase_   :				List[str]								= self.get_config()
        return config, pixel_values, labels



      def      SCREAMING_SNAKE_CASE__ (      self				:      str       ):
        return RegNetConfig(
            num_channels=self.num_channels    ,			embeddings_size=self.embeddings_size    ,			hidden_sizes=self.hidden_sizes    ,			depths=self.depths    ,			hidden_act=self.hidden_act    ,			num_labels=self.num_labels    ,			)



      def      SCREAMING_SNAKE_CASE__ (      self				:      Any    ,			SCREAMING_SNAKE_CASE_				:      List[str]    ,			SCREAMING_SNAKE_CASE_				:      List[Any]    ,			SCREAMING_SNAKE_CASE_				:      int       ):
        lowerCAmelCase_   :				List[Any]								= TFRegNetModel(config=SCREAMING_SNAKE_CASE_       )
        lowerCAmelCase_   :				List[Any]								= model(SCREAMING_SNAKE_CASE_    ,			training=SCREAMING_SNAKE_CASE_       )
        # expected last hidden states: B, C, H // 32, W // 32
        self.parent.assertEqual(
            result.last_hidden_state.shape    ,			(self.batch_size, self.hidden_sizes[-1], self.image_size // 3_2, self.image_size // 3_2)    ,			)



      def      SCREAMING_SNAKE_CASE__ (      self				:      List[str]    ,			SCREAMING_SNAKE_CASE_				:      Tuple    ,			SCREAMING_SNAKE_CASE_				:      Optional[int]    ,			SCREAMING_SNAKE_CASE_				:      Optional[Any]       ):
        lowerCAmelCase_   :				int								= self.num_labels
        lowerCAmelCase_   :				int								= TFRegNetForImageClassification(SCREAMING_SNAKE_CASE_       )
        lowerCAmelCase_   :				Dict								= model(SCREAMING_SNAKE_CASE_    ,			labels=SCREAMING_SNAKE_CASE_    ,			training=SCREAMING_SNAKE_CASE_       )
        self.parent.assertEqual(result.logits.shape    ,			(self.batch_size, self.num_labels)       )





      def      SCREAMING_SNAKE_CASE__ (      self				:      List[str]       ):
        lowerCAmelCase_   :				str								= self.prepare_config_and_inputs()
        lowerCAmelCase_						,lowerCAmelCase_						,lowerCAmelCase_   :				Tuple								= config_and_inputs
        lowerCAmelCase_   :				Optional[Any]								= {'pixel_values': pixel_values}
        return config, inputs_dict







@require_tf
class       UpperCamelCase__   (	lowercase_,					lowercase_,					unittest.TestCase  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     (TFRegNetModel, TFRegNetForImageClassification) if is_tf_available() else ()
      _SCREAMING_SNAKE_CASE  				=     (
          {"""feature-extraction""": TFRegNetModel, """image-classification""": TFRegNetForImageClassification}
          if is_tf_available()
          else {}
      )

      _SCREAMING_SNAKE_CASE  				=     False
      _SCREAMING_SNAKE_CASE  				=     False
      _SCREAMING_SNAKE_CASE  				=     False
      _SCREAMING_SNAKE_CASE  				=     False
      _SCREAMING_SNAKE_CASE  				=     False



      def      SCREAMING_SNAKE_CASE__ (      self				:      List[Any]       ):
        lowerCAmelCase_   :				List[Any]								= TFRegNetModelTester(self       )
        lowerCAmelCase_   :				Tuple								= ConfigTester(self    ,			config_class=SCREAMING_SNAKE_CASE_    ,			has_text_modality=SCREAMING_SNAKE_CASE_       )



      def      SCREAMING_SNAKE_CASE__ (      self				:      Optional[int]       ):
        return



      @unittest.skip(reason='RegNet does not use inputs_embeds'       )
      def      SCREAMING_SNAKE_CASE__ (      self				:      List[Any]       ):
        pass



      @unittest.skipIf(
          not is_tf_available() or len(tf.config.list_physical_devices('GPU'       )       ) == 0    ,			reason='TF does not support backprop for grouped convolutions on CPU.'    ,			)
      @slow
      def      SCREAMING_SNAKE_CASE__ (      self				:      Tuple       ):
        super().test_keras_fit()



      @unittest.skip(reason='RegNet does not support input and output embeddings'       )
      def      SCREAMING_SNAKE_CASE__ (      self				:      Union[str, Any]       ):
        pass



      def      SCREAMING_SNAKE_CASE__ (      self				:      int       ):
        lowerCAmelCase_						,lowerCAmelCase_   :				Optional[int]								= self.model_tester.prepare_config_and_inputs_for_common()

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

          lowerCAmelCase_   :				Any								= ['pixel_values']
          self.assertListEqual(arg_names[:1]    ,			SCREAMING_SNAKE_CASE_       )



      def      SCREAMING_SNAKE_CASE__ (      self				:      Any       ):
        lowerCAmelCase_   :				Dict								= self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_model(*SCREAMING_SNAKE_CASE_       )



      def      SCREAMING_SNAKE_CASE__ (      self				:      Optional[int]       ):
        def check_hidden_states_output(SCREAMING_SNAKE_CASE_				:      Tuple    ,			SCREAMING_SNAKE_CASE_				:      int    ,			SCREAMING_SNAKE_CASE_				:      Tuple       ):
          lowerCAmelCase_   :				List[Any]								= model_class(SCREAMING_SNAKE_CASE_       )
          lowerCAmelCase_   :				Union[str, Any]								= model(**self._prepare_for_class(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )    ,			training=SCREAMING_SNAKE_CASE_       )

          lowerCAmelCase_   :				List[str]								= outputs.encoder_hidden_states if config.is_encoder_decoder else outputs.hidden_states

          lowerCAmelCase_   :				Union[str, Any]								= self.model_tester.num_stages
          self.assertEqual(len(SCREAMING_SNAKE_CASE_       )    ,			expected_num_stages + 1       )

          # RegNet's feature maps are of shape (batch_size, num_channels, height, width)
          self.assertListEqual(
              list(hidden_states[0].shape[-2:]       )    ,			[self.model_tester.image_size // 2, self.model_tester.image_size // 2]    ,			)

        lowerCAmelCase_						,lowerCAmelCase_   :				List[Any]								= self.model_tester.prepare_config_and_inputs_for_common()
        lowerCAmelCase_   :				Optional[int]								= ['basic', 'bottleneck']
        for model_class in self.all_model_classes:
          for layer_type in layers_type:
            lowerCAmelCase_   :				str								= layer_type
            lowerCAmelCase_   :				List[str]								= True
            check_hidden_states_output(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )

            # check that output_hidden_states also work using config
            del inputs_dict["output_hidden_states"]
            lowerCAmelCase_   :				List[str]								= True

            check_hidden_states_output(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )



      def      SCREAMING_SNAKE_CASE__ (      self				:      Optional[Any]       ):
        lowerCAmelCase_						,lowerCAmelCase_   :				int								= self.model_tester.prepare_config_and_inputs_for_common()

        def check_equivalence(SCREAMING_SNAKE_CASE_				:      Dict    ,			SCREAMING_SNAKE_CASE_				:      str    ,			SCREAMING_SNAKE_CASE_				:      Optional[int]    ,			SCREAMING_SNAKE_CASE_				:      str={}       ):
          lowerCAmelCase_   :				Optional[Any]								= model(SCREAMING_SNAKE_CASE_    ,			return_dict=SCREAMING_SNAKE_CASE_    ,			**SCREAMING_SNAKE_CASE_       )
          lowerCAmelCase_   :				List[Any]								= model(SCREAMING_SNAKE_CASE_    ,			return_dict=SCREAMING_SNAKE_CASE_    ,			**SCREAMING_SNAKE_CASE_       ).to_tuple()

          def recursive_check(SCREAMING_SNAKE_CASE_				:      int    ,			SCREAMING_SNAKE_CASE_				:      int       ):
            if isinstance(SCREAMING_SNAKE_CASE_    ,			(List, Tuple)       ):
              for tuple_iterable_value, dict_iterable_value in zip(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       ):
                recursive_check(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )
            elif tuple_object is None:
              return
            else:
              self.assertTrue(
                  all(tf.equal(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )       )    ,			msg=(
                      'Tuple and dict output are not equal. Difference:'
                      F" {tf.math.reduce_max(tf.abs(tuple_object - dict_object       )       )}"
                  )    ,			)

            recursive_check(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )

        for model_class in self.all_model_classes:
          lowerCAmelCase_   :				Union[str, Any]								= model_class(SCREAMING_SNAKE_CASE_       )

          lowerCAmelCase_   :				List[Any]								= self._prepare_for_class(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )
          lowerCAmelCase_   :				Union[str, Any]								= self._prepare_for_class(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )
          check_equivalence(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )

          lowerCAmelCase_   :				Optional[int]								= self._prepare_for_class(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			return_labels=SCREAMING_SNAKE_CASE_       )
          lowerCAmelCase_   :				str								= self._prepare_for_class(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			return_labels=SCREAMING_SNAKE_CASE_       )
          check_equivalence(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )

          lowerCAmelCase_   :				Tuple								= self._prepare_for_class(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )
          lowerCAmelCase_   :				int								= self._prepare_for_class(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       )
          check_equivalence(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			{'output_hidden_states': True}       )

          lowerCAmelCase_   :				List[Any]								= self._prepare_for_class(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			return_labels=SCREAMING_SNAKE_CASE_       )
          lowerCAmelCase_   :				Any								= self._prepare_for_class(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			return_labels=SCREAMING_SNAKE_CASE_       )
          check_equivalence(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			{'output_hidden_states': True}       )



      def      SCREAMING_SNAKE_CASE__ (      self				:      Union[str, Any]       ):
        lowerCAmelCase_   :				List[str]								= self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_for_image_classification(*SCREAMING_SNAKE_CASE_       )





      @slow
      def      SCREAMING_SNAKE_CASE__ (      self				:      Union[str, Any]       ):
        for model_name in TF_REGNET_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
          lowerCAmelCase_   :				int								= TFRegNetModel.from_pretrained(SCREAMING_SNAKE_CASE_       )
          self.assertIsNotNone(SCREAMING_SNAKE_CASE_       )




def 				UpperCamelCase_    (    )						->   List[str]:

  """simple docstring"""




  lowerCAmelCase_   :				Optional[Any]								= Image.open('./tests/fixtures/tests_samples/COCO/000000039769.png'						)
  return image







@require_tf
@require_vision
class       UpperCamelCase__   (	unittest.TestCase  ):




      """simple docstring"""




      @cached_property
      def      SCREAMING_SNAKE_CASE__ (      self				:      Union[str, Any]       ):
        return (
            AutoImageProcessor.from_pretrained(TF_REGNET_PRETRAINED_MODEL_ARCHIVE_LIST[0]       )
            if is_vision_available()
            else None
        )





      @slow
      def      SCREAMING_SNAKE_CASE__ (      self				:      List[Any]       ):
        lowerCAmelCase_   :				int								= TFRegNetForImageClassification.from_pretrained(TF_REGNET_PRETRAINED_MODEL_ARCHIVE_LIST[0]       )

        lowerCAmelCase_   :				Tuple								= self.default_image_processor
        lowerCAmelCase_   :				Dict								= prepare_img()
        lowerCAmelCase_   :				Union[str, Any]								= image_processor(images=SCREAMING_SNAKE_CASE_    ,			return_tensors='tf'       )

        # forward pass
        lowerCAmelCase_   :				List[str]								= model(**SCREAMING_SNAKE_CASE_    ,			training=SCREAMING_SNAKE_CASE_       )

        # verify the logits
        lowerCAmelCase_   :				Optional[Any]								= tf.TensorShape((1, 1_0_0_0)       )
        self.assertEqual(outputs.logits.shape    ,			SCREAMING_SNAKE_CASE_       )

        lowerCAmelCase_   :				List[Any]								= tf.constant([-0.41_80, -1.50_51, -3.48_36]       )

        tf.debugging.assert_near(outputs.logits[0, :3]    ,			SCREAMING_SNAKE_CASE_    ,			atol=1E-4       )





