



from math import ceil, sqrt





def      __snake_case	(			_UpperCAmelCase = 1000000				):
    __a						       =				0

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










"""simple docstring"""
import unittest
from queue import Empty
from threading import Thread

from transformers import AutoTokenizer, TextIteratorStreamer, TextStreamer, is_torch_available
from transformers.testing_utils import CaptureStdout, require_torch, torch_device

from ..test_modeling_common import ids_tensor


if is_torch_available():
  import torch

  from transformers import AutoModelForCausalLM
@require_torch
class 							_UpperCAmelCase							( unittest.TestCase      ):





     '''simple docstring'''



     def  __lowerCAmelCase	(					self		)							->					List[str]:
         _UpperCAmelCase							:  Any											=    AutoTokenizer.from_pretrained('''hf-internal-testing/tiny-random-gpt2'''		)
         _UpperCAmelCase							:  Dict											=    AutoModelForCausalLM.from_pretrained('''hf-internal-testing/tiny-random-gpt2'''		).to(A		)
         _UpperCAmelCase							:  List[str]											=    -1

         _UpperCAmelCase							:  List[str]											=    ids_tensor((1, 5)       ,	vocab_size=model.config.vocab_size		).to(A		)
         _UpperCAmelCase							:  List[str]											=    model.generate(A       ,	max_new_tokens=1_0       ,	do_sample=A		)
         _UpperCAmelCase							:  List[Any]											=    tokenizer.decode(greedy_ids[0]		)

         with CaptureStdout() as cs:
             _UpperCAmelCase							:  str											=    TextStreamer(A		)
             model.generate(A       ,	max_new_tokens=1_0       ,	do_sample=A       ,	streamer=A		)
         # The greedy text should be printed to stdout, except for the final "\n" in the streamer
         _UpperCAmelCase							:  List[str]											=    cs.out[:-1]

         self.assertEqual(A       ,	A		)





     def  __lowerCAmelCase	(					self		)							->					Dict:
         _UpperCAmelCase							:  List[str]											=    AutoTokenizer.from_pretrained('''hf-internal-testing/tiny-random-gpt2'''		)
         _UpperCAmelCase							:  List[Any]											=    AutoModelForCausalLM.from_pretrained('''hf-internal-testing/tiny-random-gpt2'''		).to(A		)
         _UpperCAmelCase							:  List[Any]											=    -1

         _UpperCAmelCase							:  Union[str, Any]											=    ids_tensor((1, 5)       ,	vocab_size=model.config.vocab_size		).to(A		)
         _UpperCAmelCase							:  List[Any]											=    model.generate(A       ,	max_new_tokens=1_0       ,	do_sample=A		)
         _UpperCAmelCase							:  str											=    tokenizer.decode(greedy_ids[0]		)

         _UpperCAmelCase							:  Union[str, Any]											=    TextIteratorStreamer(A		)
         _UpperCAmelCase							:  Any											=    {'''input_ids''': input_ids, '''max_new_tokens''': 1_0, '''do_sample''': False, '''streamer''': streamer}
         _UpperCAmelCase							:  Any											=    Thread(target=model.generate       ,	kwargs=A		)
         thread.start()
         _UpperCAmelCase							:  Any											=    ''''''
         for new_text in streamer:
             streamer_text += new_text

         self.assertEqual(A       ,	A		)





     def  __lowerCAmelCase	(					self		)							->					str:
         _UpperCAmelCase							:  Any											=    AutoTokenizer.from_pretrained('''hf-internal-testing/tiny-random-gpt2'''		)
         _UpperCAmelCase							:  str											=    AutoModelForCausalLM.from_pretrained('''hf-internal-testing/tiny-random-gpt2'''		).to(A		)
         _UpperCAmelCase							:  Any											=    -1

         _UpperCAmelCase							:  Dict											=    ids_tensor((1, 5)       ,	vocab_size=model.config.vocab_size		).to(A		)
         _UpperCAmelCase							:  Dict											=    model.generate(A       ,	max_new_tokens=1_0       ,	do_sample=A		)
         _UpperCAmelCase							:  Dict											=    greedy_ids[:, input_ids.shape[1] :]
         _UpperCAmelCase							:  List[str]											=    tokenizer.decode(new_greedy_ids[0]		)

         with CaptureStdout() as cs:
             _UpperCAmelCase							:  Any											=    TextStreamer(A       ,	skip_prompt=A		)
             model.generate(A       ,	max_new_tokens=1_0       ,	do_sample=A       ,	streamer=A		)
         # The greedy text should be printed to stdout, except for the final "\n" in the streamer
         _UpperCAmelCase							:  Union[str, Any]											=    cs.out[:-1]

         self.assertEqual(A       ,	A		)





     def  __lowerCAmelCase	(					self		)							->					Optional[int]:
         # Tests that we can pass `decode_kwargs` to the streamer to control how the tokens are decoded. Must be tested
         # with actual models -- the dummy models' tokenizers are not aligned with their models, and
         # `skip_special_tokens=True` has no effect on them
         _UpperCAmelCase							:  int											=    AutoTokenizer.from_pretrained('''distilgpt2'''		)
         _UpperCAmelCase							:  Union[str, Any]											=    AutoModelForCausalLM.from_pretrained('''distilgpt2'''		).to(A		)
         _UpperCAmelCase							:  Tuple											=    -1

         _UpperCAmelCase							:  int											=    torch.ones((1, 5)       ,	device=A		).long() * model.config.bos_token_id
         with CaptureStdout() as cs:
             _UpperCAmelCase							:  Optional[Any]											=    TextStreamer(A       ,	skip_special_tokens=A		)
             model.generate(A       ,	max_new_tokens=1       ,	do_sample=A       ,	streamer=A		)

         # The prompt contains a special token, so the streamer should not print it. As such, the output text, when
         # re-tokenized, must only contain one token
         _UpperCAmelCase							:  Tuple											=    cs.out[:-1]  # Remove the final "\n"
         _UpperCAmelCase							:  int											=    tokenizer(A       ,	return_tensors='''pt'''		)
         self.assertEqual(streamer_text_tokenized.input_ids.shape       ,	(1, 1)		)





     def  __lowerCAmelCase	(					self		)							->					Union[str, Any]:
         _UpperCAmelCase							:  Any											=    AutoTokenizer.from_pretrained('''hf-internal-testing/tiny-random-gpt2'''		)
         _UpperCAmelCase							:  Any											=    AutoModelForCausalLM.from_pretrained('''hf-internal-testing/tiny-random-gpt2'''		).to(A		)
         _UpperCAmelCase							:  Dict											=    -1

         _UpperCAmelCase							:  str											=    ids_tensor((1, 5)       ,	vocab_size=model.config.vocab_size		).to(A		)
         _UpperCAmelCase							:  List[Any]											=    TextIteratorStreamer(A       ,	timeout=0.001		)
         _UpperCAmelCase							:  Union[str, Any]											=    {'''input_ids''': input_ids, '''max_new_tokens''': 1_0, '''do_sample''': False, '''streamer''': streamer}
         _UpperCAmelCase							:  Optional[Any]											=    Thread(target=model.generate       ,	kwargs=A		)
         thread.start()

         # The streamer will timeout after 0.001 seconds, so an exception will be raised
         with self.assertRaises(A		):
             _UpperCAmelCase							:  Optional[Any]											=    ''''''
             for new_text in streamer:
                 streamer_text += new_text


