





from collections import defaultdict
from math import ceil, sqrt




def    __UpperCAmelCase(      lowercase_ = 1_00_00_00 ,    lowercase_ = 10      ):
       _lowerCamelCase							:     defaultdict	=		defaultdict(lowercase_      )

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

              hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

              for hole_width in range(lowercase_ ,    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() = }''')








from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
    is_vision_available,
)


_lowerCamelCase			       =      {
    'configuration_layoutlmv3': [
        'LAYOUTLMV3_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'LayoutLMv3Config',
        'LayoutLMv3OnnxConfig',
    ],
    'processing_layoutlmv3': ['LayoutLMv3Processor'],
    'tokenization_layoutlmv3': ['LayoutLMv3Tokenizer'],
}

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _lowerCamelCase			       =      ['LayoutLMv3TokenizerFast']

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _lowerCamelCase			       =      [
           'LAYOUTLMV3_PRETRAINED_MODEL_ARCHIVE_LIST',
           'LayoutLMv3ForQuestionAnswering',
           'LayoutLMv3ForSequenceClassification',
           'LayoutLMv3ForTokenClassification',
           'LayoutLMv3Model',
           'LayoutLMv3PreTrainedModel',
       ]

try:
       if not is_tf_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _lowerCamelCase			       =      [
           'TF_LAYOUTLMV3_PRETRAINED_MODEL_ARCHIVE_LIST',
           'TFLayoutLMv3ForQuestionAnswering',
           'TFLayoutLMv3ForSequenceClassification',
           'TFLayoutLMv3ForTokenClassification',
           'TFLayoutLMv3Model',
           'TFLayoutLMv3PreTrainedModel',
       ]

try:
       if not is_vision_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _lowerCamelCase			       =      ['LayoutLMv3FeatureExtractor']
       _lowerCamelCase			       =      ['LayoutLMv3ImageProcessor']


if TYPE_CHECKING:
       from .configuration_layoutlmva import (
           LAYOUTLMV3_PRETRAINED_CONFIG_ARCHIVE_MAP,
           LayoutLMvaConfig,
           LayoutLMvaOnnxConfig,
       )
       from .processing_layoutlmva import LayoutLMvaProcessor
       from .tokenization_layoutlmva import LayoutLMvaTokenizer

       try:
              if not is_tokenizers_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_layoutlmva_fast import LayoutLMvaTokenizerFast

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_layoutlmva import (
                  LAYOUTLMV3_PRETRAINED_MODEL_ARCHIVE_LIST,
                  LayoutLMvaForQuestionAnswering,
                  LayoutLMvaForSequenceClassification,
                  LayoutLMvaForTokenClassification,
                  LayoutLMvaModel,
                  LayoutLMvaPreTrainedModel,
              )

       try:
              if not is_tf_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_tf_layoutlmva import (
                  TF_LAYOUTLMV3_PRETRAINED_MODEL_ARCHIVE_LIST,
                  TFLayoutLMvaForQuestionAnswering,
                  TFLayoutLMvaForSequenceClassification,
                  TFLayoutLMvaForTokenClassification,
                  TFLayoutLMvaModel,
                  TFLayoutLMvaPreTrainedModel,
              )

       try:
              if not is_vision_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .feature_extraction_layoutlmva import LayoutLMvaFeatureExtractor
              from .image_processing_layoutlmva import LayoutLMvaImageProcessor

else:
       import sys

       _lowerCamelCase			       =      _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)

