


'''simple docstring'''



from math import sqrt







def     _UpperCamelCase      (		UpperCamelCase__ = 1_0_0_0_0_0_0					):

			'''simple docstring'''





			UpperCAmelCase__  :					int        =     0
			UpperCAmelCase__  :					int        =     0
			UpperCAmelCase__  :					int

			while num_cuboids <= limit:
						max_cuboid_size += 1
						for sum_shortest_sides in range(2 ,      2 * max_cuboid_size + 1					):
									if sqrt(sum_shortest_sides**2 + max_cuboid_size**2					).is_integer():
												num_cuboids += (
												    min(UpperCamelCase__ ,      sum_shortest_sides // 2					)
												    - max(1 ,      sum_shortest_sides - max_cuboid_size					)
												    + 1
												)

			return max_cuboid_size


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



'''simple docstring'''



import unittest

from transformers import AutoTokenizer, is_flax_available
from transformers.testing_utils import require_flax, require_sentencepiece, require_tokenizers, slow


if is_flax_available():
		import jax.numpy as jnp

		from transformers import FlaxXLMRobertaModel


@require_sentencepiece
@require_tokenizers
@require_flax
class 		_snake_case					(     unittest.TestCase	):




					@slow
					def 				snake_case__						(      self):
								UpperCAmelCase__  :					Union[str, Any]        =     FlaxXLMRobertaModel.from_pretrained("""xlm-roberta-base""")
								UpperCAmelCase__  :					List[str]        =     AutoTokenizer.from_pretrained("""xlm-roberta-base""")
								UpperCAmelCase__  :					Dict        =     """The dog is cute and lives in the garden house"""
								UpperCAmelCase__  :					Dict        =     jnp.array([tokenizer.encode(_lowerCamelCase)])

								UpperCAmelCase__  :					int        =     (1, 12, 768)  # batch_size, sequence_length, embedding_vector_dim
								UpperCAmelCase__  :					Any        =     jnp.array(
								    [[-0.0101, 0.1218, -0.0803, 0.0801, 0.1327, 0.0776, -0.1215, 0.2383, 0.3338, 0.3106, 0.0300, 0.0252]])

								UpperCAmelCase__  :					Any        =     model(_lowerCamelCase)["""last_hidden_state"""]
								self.assertEqual(output.shape							,							_lowerCamelCase)
								# compare the actual values for a slice of last dim
								self.assertTrue(jnp.allclose(output[:, :, -1]							,							_lowerCamelCase							,							atol=1e-3))