
from __future__ import annotations

from math import ceil, floor, sqrt






def 		_UpperCAmelCase   (	UpperCamelCase:     int = 2_0_0_0_0_0_0  ):






	"""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() = }''')








import unittest

from transformers import DebertaVaTokenizer, DebertaVaTokenizerFast
from transformers.testing_utils import get_tests_dir, require_sentencepiece, require_tokenizers, slow

from ...test_tokenization_common import TokenizerTesterMixin


UpperCamelCase_   	=	get_tests_dir("fixtures/spiece.model")

@require_sentencepiece
@require_tokenizers
class       a		(   __UpperCAmelCase      ,	unittest.TestCase					):
							lowercase_		:						Union[str, Any]   							=  DebertaVaTokenizer
							lowercase_		:						List[str]   							=  DebertaVaTokenizerFast
							lowercase_		:						str   							=  True
							lowercase_		:						List[Any]   							=  True







							def       UpperCAmelCase__					(						self  :  Optional[Any] ):
								"""simple docstring"""







								super().setUp()

								# We have a SentencePiece fixture for testing
								__lowerCAmelCase         =							DebertaVaTokenizer(snake_case__      ,				unk_token="<unk>" )
								tokenizer.save_pretrained(self.tmpdirname )







							def       UpperCAmelCase__					(						self  :  str      ,				snake_case__  :  Dict ):
								"""simple docstring"""







								__lowerCAmelCase         =							"this is a test"
								__lowerCAmelCase         =							"this is a test"
								return input_text, output_text







							def       UpperCAmelCase__					(						self  :  int ):
								"""simple docstring"""







								__lowerCAmelCase         =							"<pad>"
								__lowerCAmelCase         =							0

								self.assertEqual(self.get_tokenizer()._convert_token_to_id(snake_case__ )      ,				snake_case__ )
								self.assertEqual(self.get_tokenizer()._convert_id_to_token(snake_case__ )      ,				snake_case__ )







							def       UpperCAmelCase__					(						self  :  Any ):
								"""simple docstring"""







								__lowerCAmelCase         =							list(self.get_tokenizer().get_vocab().keys() )
								self.assertEqual(vocab_keys[0]      ,				"<pad>" )
								self.assertEqual(vocab_keys[1]      ,				"<unk>" )
								self.assertEqual(vocab_keys[-1]      ,				"[PAD]" )
								self.assertEqual(len(snake_case__ )      ,				30_001 )







							def       UpperCAmelCase__					(						self  :  Tuple ):
								"""simple docstring"""







								self.assertEqual(self.get_tokenizer().vocab_size      ,				30_000 )







							def       UpperCAmelCase__					(						self  :  List[str] ):
								"""simple docstring"""







								__lowerCAmelCase         =							" \tHeLLo!how  \n Are yoU?  "
								__lowerCAmelCase         =							["▁hello", "!", "how", "▁are", "▁you", "?"]
								# fmt: on

								__lowerCAmelCase         =							DebertaVaTokenizer(snake_case__      ,				do_lower_case=snake_case__ )
								__lowerCAmelCase         =							tokenizer.convert_ids_to_tokens(tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )

								self.assertListEqual(snake_case__      ,				snake_case__ )

								__lowerCAmelCase         =							DebertaVaTokenizerFast(snake_case__      ,				do_lower_case=snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.convert_ids_to_tokens(rust_tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )

								self.assertListEqual(snake_case__      ,				snake_case__ )







							@unittest.skip("There is an inconsistency between slow and fast tokenizer due to a bug in the fast one." )
							def       UpperCAmelCase__					(						self  :  Union[str, Any] ):
								"""simple docstring"""







								pass







							@unittest.skip("There is an inconsistency between slow and fast tokenizer due to a bug in the fast one." )
							def       UpperCAmelCase__					(						self  :  List[str] ):
								"""simple docstring"""







								pass







							def       UpperCAmelCase__					(						self  :  Any ):
								"""simple docstring"""







								__lowerCAmelCase         =							"I was born in 92000, and this is falsé."
								__lowerCAmelCase         =							["▁", "<unk>", "▁was", "▁born", "▁in", "▁9", "2000", "▁", ",", "▁and", "▁this", "▁is", "▁fal", "s", "<unk>", "▁", ".", ]
								# fmt: on

								__lowerCAmelCase         =							DebertaVaTokenizer(snake_case__      ,				split_by_punct=snake_case__ )
								__lowerCAmelCase         =							tokenizer.convert_ids_to_tokens(tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )

								self.assertListEqual(snake_case__      ,				snake_case__ )

								__lowerCAmelCase         =							DebertaVaTokenizerFast(snake_case__      ,				split_by_punct=snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.convert_ids_to_tokens(rust_tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )

								self.assertListEqual(snake_case__      ,				snake_case__ )







							def       UpperCAmelCase__					(						self  :  Tuple ):
								"""simple docstring"""







								__lowerCAmelCase         =							"I was born in 92000, and this is falsé."
								__lowerCAmelCase         =							["▁i", "▁was", "▁born", "▁in", "▁9", "2000", "▁", ",", "▁and", "▁this", "▁is", "▁fal", "s", "<unk>", "▁", ".", ]
								# fmt: on

								__lowerCAmelCase         =							DebertaVaTokenizer(snake_case__      ,				do_lower_case=snake_case__      ,				split_by_punct=snake_case__ )
								__lowerCAmelCase         =							tokenizer.convert_ids_to_tokens(tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )
								self.assertListEqual(snake_case__      ,				snake_case__ )

								__lowerCAmelCase         =							DebertaVaTokenizerFast(snake_case__      ,				do_lower_case=snake_case__      ,				split_by_punct=snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.convert_ids_to_tokens(rust_tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )
								self.assertListEqual(snake_case__      ,				snake_case__ )







							def       UpperCAmelCase__					(						self  :  Optional[int] ):
								"""simple docstring"""







								__lowerCAmelCase         =							"I was born in 92000, and this is falsé."
								__lowerCAmelCase         =							["▁i", "▁was", "▁born", "▁in", "▁9", "2000", ",", "▁and", "▁this", "▁is", "▁fal", "s", "<unk>", ".", ]
								# fmt: on

								__lowerCAmelCase         =							DebertaVaTokenizer(snake_case__      ,				do_lower_case=snake_case__      ,				split_by_punct=snake_case__ )
								__lowerCAmelCase         =							tokenizer.convert_ids_to_tokens(tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )

								self.assertListEqual(snake_case__      ,				snake_case__ )

								__lowerCAmelCase         =							DebertaVaTokenizerFast(snake_case__      ,				do_lower_case=snake_case__      ,				split_by_punct=snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.convert_ids_to_tokens(rust_tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )

								self.assertListEqual(snake_case__      ,				snake_case__ )







							def       UpperCAmelCase__					(						self  :  int ):
								"""simple docstring"""







								__lowerCAmelCase         =							"I was born in 92000, and this is falsé."
								__lowerCAmelCase         =							["▁", "<unk>", "▁was", "▁born", "▁in", "▁9", "2000", "▁", ",", "▁and", "▁this", "▁is", "▁fal", "s", "<unk>", "▁", ".", ]
								# fmt: on

								__lowerCAmelCase         =							DebertaVaTokenizer(snake_case__      ,				do_lower_case=snake_case__      ,				split_by_punct=snake_case__ )
								__lowerCAmelCase         =							tokenizer.convert_ids_to_tokens(tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )

								self.assertListEqual(snake_case__      ,				snake_case__ )

								__lowerCAmelCase         =							DebertaVaTokenizerFast(snake_case__      ,				do_lower_case=snake_case__      ,				split_by_punct=snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.convert_ids_to_tokens(rust_tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )

								self.assertListEqual(snake_case__      ,				snake_case__ )







							def       UpperCAmelCase__					(						self  :  Tuple ):
								"""simple docstring"""







								__lowerCAmelCase         =							" \tHeLLo!how  \n Are yoU?  "
								__lowerCAmelCase         =							["▁", "<unk>", "e", "<unk>", "o", "!", "how", "▁", "<unk>", "re", "▁yo", "<unk>", "?"]
								# fmt: on

								__lowerCAmelCase         =							DebertaVaTokenizer(snake_case__      ,				do_lower_case=snake_case__      ,				split_by_punct=snake_case__ )
								__lowerCAmelCase         =							tokenizer.convert_ids_to_tokens(tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )

								self.assertListEqual(snake_case__      ,				snake_case__ )

								__lowerCAmelCase         =							DebertaVaTokenizerFast(snake_case__      ,				do_lower_case=snake_case__      ,				split_by_punct=snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.convert_ids_to_tokens(rust_tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )

								self.assertListEqual(snake_case__      ,				snake_case__ )







							def       UpperCAmelCase__					(						self  :  Optional[int] ):
								"""simple docstring"""







								__lowerCAmelCase         =							self.get_tokenizer()
								__lowerCAmelCase         =							self.get_rust_tokenizer()

								__lowerCAmelCase         =							"I was born in 92000, and this is falsé."

								__lowerCAmelCase         =							tokenizer.convert_ids_to_tokens(tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )
								__lowerCAmelCase         =							rust_tokenizer.convert_ids_to_tokens(rust_tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ ) )
								self.assertListEqual(snake_case__      ,				snake_case__ )

								__lowerCAmelCase         =							tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )

								__lowerCAmelCase         =							self.get_rust_tokenizer()
								__lowerCAmelCase         =							tokenizer.encode(snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.encode(snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )







							def       UpperCAmelCase__					(						self  :  Optional[int] ):
								"""simple docstring"""







								__lowerCAmelCase         =							"This is a test"
								__lowerCAmelCase         =							[13, 1, 4_398, 25, 21, 1_289]
								__lowerCAmelCase         =							["▁", "T", "his", "▁is", "▁a", "▁test"]
								__lowerCAmelCase         =							["▁", "<unk>", "his", "▁is", "▁a", "▁test"]

								__lowerCAmelCase         =							DebertaVaTokenizer(snake_case__      ,				keep_accents=snake_case__ )
								__lowerCAmelCase         =							DebertaVaTokenizerFast(snake_case__      ,				keep_accents=snake_case__ )

								__lowerCAmelCase         =							tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )
								__lowerCAmelCase         =							tokenizer.tokenize(snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )
								__lowerCAmelCase         =							tokenizer.convert_ids_to_tokens(snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )

								__lowerCAmelCase         =							rust_tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.tokenize(snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.convert_ids_to_tokens(snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )

								# fmt: off
								__lowerCAmelCase         =							"I was born in 92000, and this is falsé."
								__lowerCAmelCase         =							[13, 1, 23, 386, 19, 561, 3_050, 15, 17, 48, 25, 8_256, 18, 1, 9]
								__lowerCAmelCase         =							["▁", "I", "▁was", "▁born", "▁in", "▁9", "2000", ",", "▁and", "▁this", "▁is", "▁fal", "s", "é", ".", ]
								__lowerCAmelCase         =							["▁", "<unk>", "▁was", "▁born", "▁in", "▁9", "2000", ",", "▁and", "▁this", "▁is", "▁fal", "s", "<unk>", ".", ]
								# fmt: on

								__lowerCAmelCase         =							tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )
								__lowerCAmelCase         =							tokenizer.tokenize(snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )
								__lowerCAmelCase         =							tokenizer.convert_ids_to_tokens(snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )

								__lowerCAmelCase         =							rust_tokenizer.encode(snake_case__      ,				add_special_tokens=snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.tokenize(snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )
								__lowerCAmelCase         =							rust_tokenizer.convert_ids_to_tokens(snake_case__ )
								self.assertListEqual(snake_case__      ,				snake_case__ )







							def       UpperCAmelCase__					(						self  :  Any ):
								"""simple docstring"""







								__lowerCAmelCase         =							DebertaVaTokenizer(snake_case__ )

								__lowerCAmelCase         =							tokenizer.encode("sequence builders" )
								__lowerCAmelCase         =							tokenizer.encode("multi-sequence build" )

								__lowerCAmelCase         =							tokenizer.build_inputs_with_special_tokens(snake_case__ )
								__lowerCAmelCase         =							tokenizer.build_inputs_with_special_tokens(snake_case__      ,				snake_case__ )

								self.assertEqual([tokenizer.cls_token_id] + text + [tokenizer.sep_token_id]      ,				snake_case__ )
								self.assertEqual(
								    [tokenizer.cls_token_id] + text + [tokenizer.sep_token_id] + text_a + [tokenizer.sep_token_id]      ,				snake_case__      ,				)







							@slow
							def       UpperCAmelCase__					(						self  :  Optional[int] ):
								"""simple docstring"""







								__lowerCAmelCase         =							{"input_ids": [[1, 39_867, 36, 19_390, 486, 27, 35_052, 81_436, 18, 60_685, 1_225, 7, 35_052, 81_436, 18, 9_367, 16_899, 18, 15_937, 53, 594, 773, 18, 16_287, 30_465, 36, 15_937, 6, 41_139, 38, 36_979, 60_763, 191, 6, 34_132, 99, 6, 50_538, 390, 43_230, 6, 34_132, 2_779, 20_850, 14, 699, 1_072, 1_194, 36, 382, 10_901, 53, 7, 699, 1_072, 2_084, 36, 20_422, 630, 53, 19, 105, 3_049, 1_896, 1_053, 16_899, 1_506, 11, 37_978, 4_243, 7, 1_237, 31_869, 200, 16_566, 654, 6, 35_052, 81_436, 7, 55_630, 13_593, 4, 2], [1, 26, 15_011, 13, 667, 8, 1_053, 18, 23_611, 1_237, 72_356, 12_820, 34, 104_134, 1_209, 35, 13_313, 6_627, 21, 202, 347, 7, 164, 2_399, 11, 46, 4_485, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 5, 1_232, 2_864, 15_785, 14_951, 105, 5, 8_581, 1_250, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "token_type_ids": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "attention_mask": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}  # noqa: E501
								# fmt: on

								self.tokenizer_integration_test_util(
								    expected_encoding=snake_case__      ,				model_name="microsoft/deberta-v2-xlarge"      ,				revision="ad6e42c1532ddf3a15c39246b63f5559d558b670"      ,				)






