"""simple docstring"""







from __future__ import annotations

from math import ceil, floor, sqrt
def   __UpperCAmelCase				(    UpperCAmelCase_    :				int = 2_00_00_00  )							->			List[str]:

	'''simple docstring'''





	__snake_case			:							str      		= [0]
	__snake_case			:							int      		= 42

	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
	__snake_case			:							Optional[Any]      		= 0
	# the area corresponding to the grid that gives the product closest to target
	__snake_case			:							int      		= 0
	# an estimate of b, using the quadratic formula
	__snake_case			:							Any      		= 42
	# the largest integer less than b_estimate
	__snake_case			:							List[str]      		= 42
	# the largest integer less than b_estimate
	__snake_case			:							Tuple      		= 42
	# the triangle number corresponding to b_floor
	__snake_case			:							List[Any]      		= 42
	# the triangle number corresponding to b_ceil
	__snake_case			:							Union[str, Any]      		= 42

	for idx_a, triangle_a in enumerate(triangle_numbers[1:]			,							1  ):
		__snake_case			:							int      		= (-1 + sqrt(1 + 8 * target / triangle_a  )) / 2
		__snake_case			:							Dict      		= floor(__lowerCAmelCase  )
		__snake_case			:							Any      		= ceil(__lowerCAmelCase  )
		__snake_case			:							Tuple      		= triangle_numbers[b_floor]
		__snake_case			:							Dict      		= triangle_numbers[b_ceil]

		if abs(target - triangle_b_first_guess * triangle_a  ) < abs(
		    target - best_product  ):
			__snake_case			:							Union[str, Any]      		= triangle_b_first_guess * triangle_a
			__snake_case			:							str      		= idx_a * b_floor

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

	return area


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









import json
import os
import subprocess
import unittest
from ast import literal_eval

import pytest
from parameterized import parameterized_class

from . import is_sagemaker_available


if is_sagemaker_available():
						from sagemaker import Session, TrainingJobAnalytics
						from sagemaker.huggingface import HuggingFace







@pytest.mark.skipif(
    literal_eval(os.getenv('''TEST_SAGEMAKER'''	,						'''False'''      )      ) is not True	,						reason='''Skipping test because should only be run when releasing minor transformers version'''	,						)
@pytest.mark.usefixtures('''sm_env'''      )
@parameterized_class(
    [
        {
            '''framework''': '''pytorch''',
            '''script''': '''run_glue.py''',
            '''model_name_or_path''': '''distilbert-base-cased''',
            '''instance_type''': '''ml.g4dn.xlarge''',
            '''results''': {'''train_runtime''': 6_5_0, '''eval_accuracy''': 0.6, '''eval_loss''': 0.9},
        },
        {
            '''framework''': '''tensorflow''',
            '''script''': '''run_tf.py''',
            '''model_name_or_path''': '''distilbert-base-cased''',
            '''instance_type''': '''ml.g4dn.xlarge''',
            '''results''': {'''train_runtime''': 6_0_0, '''eval_accuracy''': 0.3, '''eval_loss''': 0.9},
        },
    ]      )
class        snake_case_   (unittest.TestCase      ):
					def  lowerCamelCase__(      self   :Dict      )					->    Union[str, Any]:
												if self.framework == "pytorch":
																			subprocess.run(
																			    F'cp ./examples/pytorch/text-classification/run_glue.py {self.env.test_path}/run_glue.py'.split()			,encoding='utf-8'			,check=__snake_case			,)
												assert hasattr(self			,'env'      )
					def  lowerCamelCase__(      self   :List[Any]			,__snake_case   :Optional[Any]=1      )					->    int:
												# creates estimator
												return HuggingFace(
												    entry_point=self.script			,source_dir=self.env.test_path			,role=self.env.role			,image_uri=self.env.image_uri			,base_job_name=F'{self.env.base_job_name}-single'			,instance_count=__snake_case			,instance_type=self.instance_type			,debugger_hook_config=__snake_case			,hyperparameters={**self.env.hyperparameters, 'model_name_or_path': self.model_name_or_path}			,metric_definitions=self.env.metric_definitions			,py_version='py36'			,)
					def  lowerCamelCase__(      self   :Dict			,__snake_case   :str      )					->    Optional[int]:
												TrainingJobAnalytics(__snake_case      ).export_csv(F'{self.env.test_path}/{job_name}_metrics.csv'      )



					def  lowerCamelCase__(      self   :Tuple      )					->    Union[str, Any]:
												# create estimator
												a__             =     self.create_estimator()

												# run training
												estimator.fit()

												# result dataframe
												a__             =     TrainingJobAnalytics(estimator.latest_training_job.name      ).dataframe()

												# extract kpis
												a__             =     list(result_metrics_df[result_metrics_df.metric_name == 'eval_accuracy']['value']      )
												a__             =     list(result_metrics_df[result_metrics_df.metric_name == 'eval_loss']['value']      )
												# get train time from SageMaker job, this includes starting, preprocessing, stopping
												a__             =     (
												    Session().describe_training_job(estimator.latest_training_job.name      ).get('TrainingTimeInSeconds'			,99_99_99      )
												)

												# assert kpis
												assert train_runtime <= self.results["train_runtime"]
												assert all(t >= self.results['eval_accuracy'] for t in eval_accuracy      )
												assert all(t <= self.results['eval_loss'] for t in eval_loss      )

												# dump tests result into json file to share in PR
												with open(F'{estimator.latest_training_job.name}.json'			,'w'      ) as outfile:
																			json.dump({'train_time': train_runtime, 'eval_accuracy': eval_accuracy, 'eval_loss': eval_loss}			,__snake_case      )




