




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        __SCREAMING_SNAKE_CASE(     self    ):




											"""simple docstring"""



											__lowerCAmelCase            = TFAutoModelForSeqaSeqLM.from_pretrained("google/mt5-small"    )
											__lowerCAmelCase            = AutoTokenizer.from_pretrained("google/mt5-small"    )

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

											__lowerCAmelCase            = model(_A	,    labels=_A    ).loss
											__lowerCAmelCase            = -tf.math.reduce_mean(_A    ).numpy()

											__lowerCAmelCase            = -21.22_81_68
											self.assertTrue(abs(mtf_score - EXPECTED_SCORE    ) < 2E-4    )










from math import ceil, sqrt







def 			_a   (		SCREAMING_SNAKE_CASE_							:       int = 1_00_00_00  ):
					__lowerCAmelCase            = 0

					for outer_width in range(3   ,   (limit // 4) + 2  ):
										if outer_width**2 > limit:
															__lowerCAmelCase            = max(ceil(sqrt(outer_width**2 - limit  )  )   ,   1  )
										else:
															__lowerCAmelCase            = 1
										if (outer_width - hole_width_lower_bound) % 2:
															hole_width_lower_bound += 1

										answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

					return answer


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




