




"""simple docstring"""





from __future__ import annotations

from math import ceil, floor, sqrt

def        _UpperCamelCase     (      UpperCamelCase = 200_0000				)      ->      int:


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

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

						if abs(target - triangle_b_first_guess * triangle_a				) < abs(
						    target - best_product				):
									__UpperCAmelCase						:			List[str]												=       triangle_b_first_guess * triangle_a
									__UpperCAmelCase						:			int												=       idx_a * b_floor

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

			return area


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








import subprocess
import sys

from transformers import BertConfig, BertModel, BertTokenizer, pipeline
from transformers.testing_utils import TestCasePlus, require_torch





class 			lowerCamelCase_				( _SCREAMING_SNAKE_CASE   ):


 '''simple docstring'''







 @require_torch
 def  lowerCAmelCase_    (				self    :						int		):
       # this test is a bit tricky since TRANSFORMERS_OFFLINE can only be changed before
       # `transformers` is loaded, and it's too late for inside pytest - so we are changing it
       # while running an external program

       # python one-liner segments

       # this must be loaded before socket.socket is monkey-patched
       SCREAMING_SNAKE_CASE_      		=     '\nfrom transformers import BertConfig, BertModel, BertTokenizer, pipeline\n        '

       SCREAMING_SNAKE_CASE_      		=     '\nmname = "hf-internal-testing/tiny-random-bert"\nBertConfig.from_pretrained(mname)\nBertModel.from_pretrained(mname)\nBertTokenizer.from_pretrained(mname)\npipe = pipeline(task="fill-mask", model=mname)\nprint("success")\n        '

       SCREAMING_SNAKE_CASE_      		=     '\nimport socket\ndef offline_socket(*args, **kwargs): raise RuntimeError("Offline mode is enabled, we shouldn\'t access internet")\nsocket.socket = offline_socket\n        '

       # Force fetching the files so that we can use the cache
       SCREAMING_SNAKE_CASE_      		=     'hf-internal-testing/tiny-random-bert'
       BertConfig.from_pretrained(_lowerCAmelCase		)
       BertModel.from_pretrained(_lowerCAmelCase		)
       BertTokenizer.from_pretrained(_lowerCAmelCase		)
       pipeline(task='fill-mask'							,							model=_lowerCAmelCase		)

       # baseline - just load from_pretrained with normal network
       SCREAMING_SNAKE_CASE_      		=     [sys.executable, '-c', '\n'.join([load, run, mock]		)]

       # should succeed
       SCREAMING_SNAKE_CASE_      		=     self.get_env()
       # should succeed as TRANSFORMERS_OFFLINE=1 tells it to use local files
       SCREAMING_SNAKE_CASE_      		=     '1'
       SCREAMING_SNAKE_CASE_      		=     subprocess.run(_lowerCAmelCase							,							env=_lowerCAmelCase							,							check=_lowerCAmelCase							,							capture_output=_lowerCAmelCase		)
       self.assertEqual(result.returncode							,							0							,							result.stderr		)
       self.assertIn('success'							,							result.stdout.decode()		)



 @require_torch
 def  lowerCAmelCase_    (				self    :						Tuple		):
       # python one-liner segments
       # this must be loaded before socket.socket is monkey-patched
       SCREAMING_SNAKE_CASE_      		=     '\nfrom transformers import BertConfig, BertModel, BertTokenizer, pipeline\n        '

       SCREAMING_SNAKE_CASE_      		=     '\nmname = "hf-internal-testing/tiny-random-bert"\nBertConfig.from_pretrained(mname)\nBertModel.from_pretrained(mname)\nBertTokenizer.from_pretrained(mname)\npipe = pipeline(task="fill-mask", model=mname)\nprint("success")\n        '

       SCREAMING_SNAKE_CASE_      		=     '\nimport socket\ndef offline_socket(*args, **kwargs): raise socket.error("Faking flaky internet")\nsocket.socket = offline_socket\n        '

       # Force fetching the files so that we can use the cache
       SCREAMING_SNAKE_CASE_      		=     'hf-internal-testing/tiny-random-bert'
       BertConfig.from_pretrained(_lowerCAmelCase		)
       BertModel.from_pretrained(_lowerCAmelCase		)
       BertTokenizer.from_pretrained(_lowerCAmelCase		)
       pipeline(task='fill-mask'							,							model=_lowerCAmelCase		)

       # baseline - just load from_pretrained with normal network
       SCREAMING_SNAKE_CASE_      		=     [sys.executable, '-c', '\n'.join([load, run, mock]		)]

       # should succeed
       SCREAMING_SNAKE_CASE_      		=     self.get_env()
       SCREAMING_SNAKE_CASE_      		=     subprocess.run(_lowerCAmelCase							,							env=_lowerCAmelCase							,							check=_lowerCAmelCase							,							capture_output=_lowerCAmelCase		)
       self.assertEqual(result.returncode							,							0							,							result.stderr		)
       self.assertIn('success'							,							result.stdout.decode()		)



 @require_torch
 def  lowerCAmelCase_    (				self    :						List[str]		):
       # this test is a bit tricky since TRANSFORMERS_OFFLINE can only be changed before
       # `transformers` is loaded, and it's too late for inside pytest - so we are changing it
       # while running an external program

       # python one-liner segments

       # this must be loaded before socket.socket is monkey-patched
       SCREAMING_SNAKE_CASE_      		=     '\nfrom transformers import BertConfig, BertModel, BertTokenizer\n        '

       SCREAMING_SNAKE_CASE_      		=     '\nmname = "hf-internal-testing/tiny-random-bert-sharded"\nBertConfig.from_pretrained(mname)\nBertModel.from_pretrained(mname)\nprint("success")\n        '

       SCREAMING_SNAKE_CASE_      		=     '\nimport socket\ndef offline_socket(*args, **kwargs): raise ValueError("Offline mode is enabled")\nsocket.socket = offline_socket\n        '

       # baseline - just load from_pretrained with normal network
       SCREAMING_SNAKE_CASE_      		=     [sys.executable, '-c', '\n'.join([load, run]		)]

       # should succeed
       SCREAMING_SNAKE_CASE_      		=     self.get_env()
       SCREAMING_SNAKE_CASE_      		=     subprocess.run(_lowerCAmelCase							,							env=_lowerCAmelCase							,							check=_lowerCAmelCase							,							capture_output=_lowerCAmelCase		)
       self.assertEqual(result.returncode							,							0							,							result.stderr		)
       self.assertIn('success'							,							result.stdout.decode()		)

       # next emulate no network
       SCREAMING_SNAKE_CASE_      		=     [sys.executable, '-c', '\n'.join([load, mock, run]		)]

       # Doesn't fail anymore since the model is in the cache due to other tests, so commenting this.
       # env["TRANSFORMERS_OFFLINE"] = "0"
       # result = subprocess.run(cmd, env=env, check=False, capture_output=True)
       # self.assertEqual(result.returncode, 1, result.stderr)

       # should succeed as TRANSFORMERS_OFFLINE=1 tells it to use local files
       SCREAMING_SNAKE_CASE_      		=     '1'
       SCREAMING_SNAKE_CASE_      		=     subprocess.run(_lowerCAmelCase							,							env=_lowerCAmelCase							,							check=_lowerCAmelCase							,							capture_output=_lowerCAmelCase		)
       self.assertEqual(result.returncode							,							0							,							result.stderr		)
       self.assertIn('success'							,							result.stdout.decode()		)



 @require_torch
 def  lowerCAmelCase_    (				self    :						Any		):
       SCREAMING_SNAKE_CASE_      		=     '\nfrom transformers import pipeline\n        '
       SCREAMING_SNAKE_CASE_      		=     '\nmname = "hf-internal-testing/tiny-random-bert"\npipe = pipeline(model=mname)\n        '

       SCREAMING_SNAKE_CASE_      		=     '\nimport socket\ndef offline_socket(*args, **kwargs): raise socket.error("Offline mode is enabled")\nsocket.socket = offline_socket\n        '
       SCREAMING_SNAKE_CASE_      		=     self.get_env()
       SCREAMING_SNAKE_CASE_      		=     '1'
       SCREAMING_SNAKE_CASE_      		=     [sys.executable, '-c', '\n'.join([load, mock, run]		)]
       SCREAMING_SNAKE_CASE_      		=     subprocess.run(_lowerCAmelCase							,							env=_lowerCAmelCase							,							check=_lowerCAmelCase							,							capture_output=_lowerCAmelCase		)
       self.assertEqual(result.returncode							,							1							,							result.stderr		)
       self.assertIn(
           'You cannot infer task automatically within `pipeline` when using offline mode'							,							result.stderr.decode().replace('\n'							,							''		)							,							)




 @require_torch
 def  lowerCAmelCase_    (				self    :						Optional[int]		):
       SCREAMING_SNAKE_CASE_      		=     '\nfrom transformers import AutoModel\n        '
       SCREAMING_SNAKE_CASE_      		=     '\nmname = "hf-internal-testing/test_dynamic_model"\nAutoModel.from_pretrained(mname, trust_remote_code=True)\nprint("success")\n        '

       # baseline - just load from_pretrained with normal network
       SCREAMING_SNAKE_CASE_      		=     [sys.executable, '-c', '\n'.join([load, run]		)]

       # should succeed
       SCREAMING_SNAKE_CASE_      		=     self.get_env()
       SCREAMING_SNAKE_CASE_      		=     subprocess.run(_lowerCAmelCase							,							env=_lowerCAmelCase							,							check=_lowerCAmelCase							,							capture_output=_lowerCAmelCase		)
       self.assertEqual(result.returncode							,							0							,							result.stderr		)
       self.assertIn('success'							,							result.stdout.decode()		)

       # should succeed as TRANSFORMERS_OFFLINE=1 tells it to use local files
       SCREAMING_SNAKE_CASE_      		=     '1'
       SCREAMING_SNAKE_CASE_      		=     subprocess.run(_lowerCAmelCase							,							env=_lowerCAmelCase							,							check=_lowerCAmelCase							,							capture_output=_lowerCAmelCase		)
       self.assertEqual(result.returncode							,							0							,							result.stderr		)
       self.assertIn('success'							,							result.stdout.decode()		)