
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
					from transformers import AutoModelForSeqaSeqLM, AutoTokenizer

@require_torch
@require_sentencepiece
@require_tokenizers
class       a		(   unittest.TestCase					):







							@slow
							def       UpperCAmelCase__					(						self  :  List[Any] ):
								"""simple docstring"""







								__lowerCAmelCase         =							AutoModelForSeqaSeqLM.from_pretrained("google/mt5-small"      ,				return_dict=snake_case__ ).to(snake_case__ )
								__lowerCAmelCase         =							AutoTokenizer.from_pretrained("google/mt5-small" )

								__lowerCAmelCase         =							tokenizer("Hello there"      ,				return_tensors="pt" ).input_ids
								__lowerCAmelCase         =							tokenizer("Hi I am"      ,				return_tensors="pt" ).input_ids

								__lowerCAmelCase         =							model(input_ids.to(snake_case__ )      ,				labels=labels.to(snake_case__ ) ).loss
								__lowerCAmelCase         =							-(labels.shape[-1] * loss.item())

								__lowerCAmelCase         =							-8_4.9_1_2_7
								self.assertTrue(abs(mtf_score - EXPECTED_SCORE ) < 1E-4 )








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() = }''')






