




from __future__ import annotations

from math import ceil, floor, sqrt

def lowercase    (  SCREAMING_SNAKE_CASE = 2_00_00_00 )			->							int:


			'''simple docstring'''







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

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

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

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

			return area


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






from __future__ import annotations

import unittest

from transformers import is_tf_available
from transformers.testing_utils import require_sentencepiece, require_tf, require_tokenizers, slow


if is_tf_available():
				import tensorflow as tf

				from transformers import AutoTokenizer, TFAutoModelForSeqaSeqLM



@require_tf
@require_sentencepiece
@require_tokenizers
class       a_       (     unittest.TestCase     ):





	@slow
	def 						A_(							self      )  ->					str:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						TFAutoModelForSeqaSeqLM.from_pretrained('google/mt5-small'      )
				SCREAMING_SNAKE_CASE_								=						AutoTokenizer.from_pretrained('google/mt5-small'      )

				SCREAMING_SNAKE_CASE_								=						tokenizer('Hello there'      ,     return_tensors='tf'      ).input_ids
				SCREAMING_SNAKE_CASE_								=						tokenizer('Hi I am'      ,     return_tensors='tf'      ).input_ids

				SCREAMING_SNAKE_CASE_								=						model(SCREAMING_SNAKE_CASE      ,     labels=SCREAMING_SNAKE_CASE      ).loss
				SCREAMING_SNAKE_CASE_								=						-tf.math.reduce_mean(SCREAMING_SNAKE_CASE      ).numpy()

				SCREAMING_SNAKE_CASE_								=						-2_1.2_2_8_1_6_8
				self.assertTrue(abs(mtf_score - EXPECTED_SCORE      ) < 2e-4      )
