






import time
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch, torch_device

from ..test_modeling_common import ids_tensor


if is_torch_available():
     import torch

     from transformers.generation import (
         MaxLengthCriteria,
         MaxNewTokensCriteria,
         MaxTimeCriteria,
         StoppingCriteriaList,
         validate_stopping_criteria,
     )






@require_torch
class 		lowercase_					(	unittest.TestCase   ):






      '''simple docstring'''




      def       __lowerCAmelCase					(      self      :						int ,					__UpperCAmelCase      :						Union[str, Any]  )    ->Union[str, Any]:




       """simple docstring"""


       a		  =      3
       a		  =      250

       a		  =      ids_tensor((batch_size, length) ,					lowerCAmelCase__  )
       a		  =      torch.ones((batch_size, length) ,					device=lowerCAmelCase__ ,					dtype=torch.float  ) / length
       return input_ids, scores







      def       __lowerCAmelCase					(      self      :						Union[str, Any]  )    ->Optional[int]:




       """simple docstring"""


       a		  =      self._get_tensors(5  )

       a		  =      StoppingCriteriaList(
           [
               MaxLengthCriteria(max_length=10  ),
               MaxTimeCriteria(max_time=0.1  ),
           ]  )

       self.assertFalse(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )

       a		  =      self._get_tensors(9  )
       self.assertFalse(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )

       a		  =      self._get_tensors(10  )
       self.assertTrue(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )







      def       __lowerCAmelCase					(      self      :						str  )    ->str:




       """simple docstring"""


       a		  =      MaxLengthCriteria(max_length=10  )

       a		  =      self._get_tensors(5  )
       self.assertFalse(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )

       a		  =      self._get_tensors(9  )
       self.assertFalse(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )

       a		  =      self._get_tensors(10  )
       self.assertTrue(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )







      def       __lowerCAmelCase					(      self      :						List[Any]  )    ->Optional[int]:




       """simple docstring"""


       a		  =      MaxNewTokensCriteria(start_length=5 ,					max_new_tokens=5  )

       a		  =      self._get_tensors(5  )
       self.assertFalse(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )

       a		  =      self._get_tensors(9  )
       self.assertFalse(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )

       a		  =      self._get_tensors(10  )
       self.assertTrue(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )

       a		  =      StoppingCriteriaList([criteria]  )
       self.assertEqual(criteria_list.max_length ,					10  )







      def       __lowerCAmelCase					(      self      :						Dict  )    ->int:




       """simple docstring"""


       a		  =      self._get_tensors(5  )

       a		  =      MaxTimeCriteria(max_time=0.1  )
       self.assertFalse(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )

       a		  =      MaxTimeCriteria(max_time=0.1 ,					initial_timestamp=time.time() - 0.2  )
       self.assertTrue(criteria(lowerCAmelCase__ ,					lowerCAmelCase__  )  )







      def       __lowerCAmelCase					(      self      :						List[Any]  )    ->Any:




       """simple docstring"""


       validate_stopping_criteria(StoppingCriteriaList([MaxLengthCriteria(10  )]  ) ,					10  )

       with self.assertWarns(lowerCAmelCase__  ):
        validate_stopping_criteria(StoppingCriteriaList([MaxLengthCriteria(10  )]  ) ,					11  )

       a		  =      validate_stopping_criteria(StoppingCriteriaList() ,					11  )

       self.assertEqual(len(lowerCAmelCase__  ) ,					1  )







'''simple docstring'''




from math import ceil, sqrt


def 				lowerCAmelCase_   (	_lowerCamelCase:   int = 1_00_00_00					):
		__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		0

		for outer_width in range(3       ,      (limit // 4) + 2					):
				if outer_width**2 > limit:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		max(ceil(sqrt(outer_width**2 - limit					)					)       ,      1					)
				else:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		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() = }")