


'''simple docstring'''
from collections import defaultdict
from math import ceil, sqrt


def 			_lowercase       (				UpperCamelCase__       :					int = 1000000,				UpperCamelCase__       :					int = 10			):
 __A  :		defaultdict       =			defaultdict(UpperCamelCase__			)

 for outer_width in range(3,				(t_limit // 4) + 2			):
  if outer_width * outer_width > t_limit:
   __A  :		Optional[int]       =			max(
       ceil(sqrt(outer_width * outer_width - t_limit			)			),				1			)
  else:
   __A  :		Optional[Any]       =			1

  hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

  for hole_width in range(UpperCamelCase__,				outer_width - 1,				2			):
   count[outer_width * outer_width - hole_width * hole_width] += 1

 return sum(1 for n in count.values() if 1 <= n <= 10			)


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










'''simple docstring'''
import shutil
import tempfile
import unittest

import numpy as np
import pytest

from transformers.testing_utils import require_vision
from transformers.utils import is_vision_available


if is_vision_available():
 from PIL import Image

 from transformers import AutoProcessor, BertTokenizer, BlipImageProcessor, BlipProcessor, PreTrainedTokenizerFast

@require_vision
class 						_lowerCamelCase					(    unittest.TestCase				):




 '''simple docstring'''


 def  snake_case__   (      self						):

  """simple docstring"""







  __A  :		int       =			tempfile.mkdtemp()

  __A  :		List[Any]       =			BlipImageProcessor()
  __A  :		List[str]       =			BertTokenizer.from_pretrained('hf-internal-testing/tiny-random-BertModel'						)

  __A  :		Union[str, Any]       =			BlipProcessor(__lowercase      ,      __lowercase						)

  processor.save_pretrained(self.tmpdirname						)


 def  snake_case__   (      self      ,      **__lowercase						):

  """simple docstring"""







  return AutoProcessor.from_pretrained(self.tmpdirname      ,      **__lowercase						).tokenizer


 def  snake_case__   (      self      ,      **__lowercase						):

  """simple docstring"""







  return AutoProcessor.from_pretrained(self.tmpdirname      ,      **__lowercase						).image_processor


 def  snake_case__   (      self						):

  """simple docstring"""







  shutil.rmtree(self.tmpdirname						)


 def  snake_case__   (      self						):

  """simple docstring"""







  __A  :		Optional[Any]       =			[np.random.randint(255      ,      size=(3, 30, 400)      ,      dtype=np.uinta						)]

  __A  :		Union[str, Any]       =			[Image.fromarray(np.moveaxis(__lowercase      ,      0      ,      -1						)						) for x in image_inputs]

  return image_inputs


 def  snake_case__   (      self						):

  """simple docstring"""







  __A  :		Any       =			BlipProcessor(tokenizer=self.get_tokenizer()      ,      image_processor=self.get_image_processor()						)
  processor.save_pretrained(self.tmpdirname						)

  __A  :		Optional[int]       =			self.get_tokenizer(bos_token='(BOS)'      ,      eos_token='(EOS)'						)
  __A  :		Optional[Any]       =			self.get_image_processor(do_normalize=__lowercase      ,      padding_value=1.0						)

  __A  :		List[str]       =			BlipProcessor.from_pretrained(
      self.tmpdirname      ,      bos_token='(BOS)'      ,      eos_token='(EOS)'      ,      do_normalize=__lowercase      ,      padding_value=1.0						)

  self.assertEqual(processor.tokenizer.get_vocab()      ,      tokenizer_add_kwargs.get_vocab()						)
  self.assertIsInstance(processor.tokenizer      ,      __lowercase						)

  self.assertEqual(processor.image_processor.to_json_string()      ,      image_processor_add_kwargs.to_json_string()						)
  self.assertIsInstance(processor.image_processor      ,      __lowercase						)


 def  snake_case__   (      self						):

  """simple docstring"""







  __A  :		Optional[Any]       =			self.get_image_processor()
  __A  :		Union[str, Any]       =			self.get_tokenizer()

  __A  :		Dict       =			BlipProcessor(tokenizer=__lowercase      ,      image_processor=__lowercase						)

  __A  :		Dict       =			self.prepare_image_inputs()

  __A  :		str       =			image_processor(__lowercase      ,      return_tensors='np'						)
  __A  :		List[Any]       =			processor(images=__lowercase      ,      return_tensors='np'						)

  for key in input_feat_extract.keys():
   self.assertAlmostEqual(input_feat_extract[key].sum()      ,      input_processor[key].sum()      ,      delta=1E-2						)


 def  snake_case__   (      self						):

  """simple docstring"""







  __A  :		int       =			self.get_image_processor()
  __A  :		List[str]       =			self.get_tokenizer()

  __A  :		str       =			BlipProcessor(tokenizer=__lowercase      ,      image_processor=__lowercase						)

  __A  :		List[Any]       =			'lower newer'

  __A  :		Any       =			processor(text=__lowercase						)

  __A  :		int       =			tokenizer(__lowercase      ,      return_token_type_ids=__lowercase						)

  for key in encoded_tok.keys():
   self.assertListEqual(encoded_tok[key]      ,      encoded_processor[key]						)


 def  snake_case__   (      self						):

  """simple docstring"""







  __A  :		str       =			self.get_image_processor()
  __A  :		Dict       =			self.get_tokenizer()

  __A  :		Any       =			BlipProcessor(tokenizer=__lowercase      ,      image_processor=__lowercase						)

  __A  :		List[Any]       =			'lower newer'
  __A  :		List[str]       =			self.prepare_image_inputs()

  __A  :		Optional[Any]       =			processor(text=__lowercase      ,      images=__lowercase						)

  self.assertListEqual(list(inputs.keys()						)      ,      ['pixel_values', 'input_ids', 'attention_mask']						)

  # test if it raises when no input is passed
  with pytest.raises(__lowercase						):
   processor()


 def  snake_case__   (      self						):

  """simple docstring"""







  __A  :		int       =			self.get_image_processor()
  __A  :		Optional[int]       =			self.get_tokenizer()

  __A  :		List[str]       =			BlipProcessor(tokenizer=__lowercase      ,      image_processor=__lowercase						)

  __A  :		str       =			[[1, 4, 5, 8, 1, 0, 8], [3, 4, 3, 1, 1, 8, 9]]

  __A  :		Tuple       =			processor.batch_decode(__lowercase						)
  __A  :		Tuple       =			tokenizer.batch_decode(__lowercase						)

  self.assertListEqual(__lowercase      ,      __lowercase						)







 def  snake_case__   (      self						):

  """simple docstring"""







  __A  :		Optional[int]       =			self.get_image_processor()
  __A  :		Any       =			self.get_tokenizer()

  __A  :		Any       =			BlipProcessor(tokenizer=__lowercase      ,      image_processor=__lowercase						)

  __A  :		Optional[int]       =			'lower newer'
  __A  :		List[str]       =			self.prepare_image_inputs()

  __A  :		int       =			processor(text=__lowercase      ,      images=__lowercase						)

  # For now the processor supports only ['pixel_values', 'input_ids', 'attention_mask']
  self.assertListEqual(list(inputs.keys()						)      ,      ['pixel_values', 'input_ids', 'attention_mask']						)






