




from __future__ import annotations

from math import ceil, floor, sqrt







def 			lowerCamelCase_		(       UpperCamelCase__				:      int = 200_0000      )     ->       int:





				"""simple docstring"""


				__lowerCamelCase		       =    [0]
				__lowerCamelCase		       =    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
				__lowerCamelCase		       =    0
				# the area corresponding to the grid that gives the product closest to target
				__lowerCamelCase		       =    0
				# an estimate of b, using the quadratic formula
				__lowerCamelCase		       =    42
				# the largest integer less than b_estimate
				__lowerCamelCase		       =    42
				# the largest integer less than b_estimate
				__lowerCamelCase		       =    42
				# the triangle number corresponding to b_floor
				__lowerCamelCase		       =    42
				# the triangle number corresponding to b_ceil
				__lowerCamelCase		       =    42

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

								if abs(target - triangle_b_first_guess * triangle_a      ) < abs(
								    target - best_product      ):
												__lowerCamelCase		       =    triangle_b_first_guess * triangle_a
												__lowerCamelCase		       =    idx_a * b_floor

								if abs(target - triangle_b_second_guess * triangle_a      ) < abs(
								    target - best_product      ):
												__lowerCamelCase		       =    triangle_b_second_guess * triangle_a
												__lowerCamelCase		       =    idx_a * b_ceil

				return area


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




"""simple docstring"""





from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType
class 						SCREAMING_SNAKE_CASE_ (						__a ):




		"""simple docstring"""





		__lowercase							:  List[Any]						   =		['''image_processor''', '''tokenizer''']
		__lowercase							:  List[Any]						   =		'''BridgeTowerImageProcessor'''
		__lowercase							:  Tuple						   =		('''RobertaTokenizer''', '''RobertaTokenizerFast''')




		def __init__(     self							,  lowerCAmelCase__							,  lowerCAmelCase__):
				super().__init__(lowerCAmelCase__							,  lowerCAmelCase__)




		def __call__(     self							,  lowerCAmelCase__							,  lowerCAmelCase__ = None							,  lowerCAmelCase__ = True							,  lowerCAmelCase__ = False							,  lowerCAmelCase__ = None							,  lowerCAmelCase__ = None							,  lowerCAmelCase__ = 0							,  lowerCAmelCase__ = None							,  lowerCAmelCase__ = None							,  lowerCAmelCase__ = None							,  lowerCAmelCase__ = False							,  lowerCAmelCase__ = False							,  lowerCAmelCase__ = False							,  lowerCAmelCase__ = False							,  lowerCAmelCase__ = True							,  lowerCAmelCase__ = None							,  **lowerCAmelCase__							,  ):
				__SCREAMING_SNAKE_CASE            = self.tokenizer(
				    text=lowerCAmelCase__							,  add_special_tokens=lowerCAmelCase__							,  padding=lowerCAmelCase__							,  truncation=lowerCAmelCase__							,  max_length=lowerCAmelCase__							,  stride=lowerCAmelCase__							,  pad_to_multiple_of=lowerCAmelCase__							,  return_token_type_ids=lowerCAmelCase__							,  return_attention_mask=lowerCAmelCase__							,  return_overflowing_tokens=lowerCAmelCase__							,  return_special_tokens_mask=lowerCAmelCase__							,  return_offsets_mapping=lowerCAmelCase__							,  return_length=lowerCAmelCase__							,  verbose=lowerCAmelCase__							,  return_tensors=lowerCAmelCase__							,  **lowerCAmelCase__							,  )
				# add pixel_values + pixel_mask
				__SCREAMING_SNAKE_CASE            = self.image_processor(
				    lowerCAmelCase__							,  return_tensors=lowerCAmelCase__							,  do_normalize=lowerCAmelCase__							,  do_center_crop=lowerCAmelCase__							,  **lowerCAmelCase__)
				encoding.update(lowerCAmelCase__)

				return encoding




		def 	snake_case_     (     self							,  *lowerCAmelCase__							,  **lowerCAmelCase__):
				return self.tokenizer.batch_decode(*lowerCAmelCase__							,  **lowerCAmelCase__)




		def 	snake_case_     (     self							,  *lowerCAmelCase__							,  **lowerCAmelCase__):
				return self.tokenizer.decode(*lowerCAmelCase__							,  **lowerCAmelCase__)




		@property
		def 	snake_case_     (     self):
				__SCREAMING_SNAKE_CASE            = self.tokenizer.model_input_names
				__SCREAMING_SNAKE_CASE            = self.image_processor.model_input_names
				return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names))




