code: 
  
  """simple docstring"""
  from __future__ import annotations
  
  from pathlib import Path
  
  
  
  
  def 				a__	(	lowerCAmelCase ,  lowerCAmelCase						)  ->   int:
        return pointa[0] * pointa[1] - pointa[1] * pointa[0]
  
  
  
  
  def 				a__	(	lowerCAmelCase ,  lowerCAmelCase ,  lowerCAmelCase ,  lowerCAmelCase ,  lowerCAmelCase ,  lowerCAmelCase						)  ->   bool:
        UpperCAmelCase__ :       tuple[int, int]						=						(xa, ya)
        UpperCAmelCase__ :       tuple[int, int]						=						(xa - xa, ya - ya)
        UpperCAmelCase__ :       tuple[int, int]						=						(xa - xa, ya - ya)
        UpperCAmelCase__ :       float						=						-vector_product(lowerCAmelCase ,  lowerCAmelCase						) / vector_product(
            lowerCAmelCase ,  lowerCAmelCase						)
        UpperCAmelCase__ :       float						=						+vector_product(lowerCAmelCase ,  lowerCAmelCase						) / vector_product(
            lowerCAmelCase ,  lowerCAmelCase						)
  
        return a > 0 and b > 0 and a + b < 1
  
  
  
  
  def 				a__	(	lowerCAmelCase = "p102_triangles.txt"						)  ->   int:
        UpperCAmelCase__ :       str						=						Path(lowerCAmelCase						).parent.joinpath(lowerCAmelCase						).read_text(encoding="""utf-8"""						)
  
        UpperCAmelCase__ :       list[list[int]]						=						[]
        for line in data.strip().split("""\n"""						):
              triangles.append([int(lowerCAmelCase						) for number in line.split(""","""						)]						)
  
        UpperCAmelCase__ :       int						=						0
        UpperCAmelCase__ :       list[int]
  
        for triangle in triangles:
              ret += contains_origin(*lowerCAmelCase						)
  
        return ret
  
  
  if __name__ == "__main__":
      print(f'''{solution() = }''')
  
  
style_context: 
  
  """simple docstring"""
  from typing import TYPE_CHECKING
  
  from ...utils import (
      OptionalDependencyNotAvailable,
      _LazyModule,
      is_flax_available,
      is_keras_nlp_available,
      is_tensorflow_text_available,
      is_tf_available,
      is_tokenizers_available,
      is_torch_available,
  )
  
  
  _A						=     {
      """configuration_gpt2""": ["""GPT2_PRETRAINED_CONFIG_ARCHIVE_MAP""", """GPT2Config""", """GPT2OnnxConfig"""],
      """tokenization_gpt2""": ["""GPT2Tokenizer"""],
  }
  
  try:
      if not is_tokenizers_available():
          raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
      pass
  else:
      _A						=     ["""GPT2TokenizerFast"""]
  
  try:
      if not is_torch_available():
          raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
      pass
  else:
      _A						=     [
          """GPT2_PRETRAINED_MODEL_ARCHIVE_LIST""",
          """GPT2DoubleHeadsModel""",
          """GPT2ForQuestionAnswering""",
          """GPT2ForSequenceClassification""",
          """GPT2ForTokenClassification""",
          """GPT2LMHeadModel""",
          """GPT2Model""",
          """GPT2PreTrainedModel""",
          """load_tf_weights_in_gpt2""",
      ]
  
  try:
      if not is_tf_available():
          raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
      pass
  else:
      _A						=     [
          """TF_GPT2_PRETRAINED_MODEL_ARCHIVE_LIST""",
          """TFGPT2DoubleHeadsModel""",
          """TFGPT2ForSequenceClassification""",
          """TFGPT2LMHeadModel""",
          """TFGPT2MainLayer""",
          """TFGPT2Model""",
          """TFGPT2PreTrainedModel""",
      ]
  
  try:
      if not is_keras_nlp_available():
          raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
      pass
  else:
      _A						=     ["""TFGPT2Tokenizer"""]
  
  try:
      if not is_flax_available():
          raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
      pass
  else:
      _A						=     ["""FlaxGPT2LMHeadModel""", """FlaxGPT2Model""", """FlaxGPT2PreTrainedModel"""]
  
  if TYPE_CHECKING:
      from .configuration_gpta import GPT2_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTaConfig, GPTaOnnxConfig
      from .tokenization_gpta import GPTaTokenizer
  
      try:
          if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
          pass
      else:
          from .tokenization_gpta_fast import GPTaTokenizerFast
  
      try:
          if not is_torch_available():
              raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
          pass
      else:
          from .modeling_gpta import (
              GPT2_PRETRAINED_MODEL_ARCHIVE_LIST,
              GPTaDoubleHeadsModel,
              GPTaForQuestionAnswering,
              GPTaForSequenceClassification,
              GPTaForTokenClassification,
              GPTaLMHeadModel,
              GPTaModel,
              GPTaPreTrainedModel,
              load_tf_weights_in_gpta,
          )
  
      try:
          if not is_tf_available():
              raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
          pass
      else:
          from .modeling_tf_gpta import (
              TF_GPT2_PRETRAINED_MODEL_ARCHIVE_LIST,
              TFGPTaDoubleHeadsModel,
              TFGPTaForSequenceClassification,
              TFGPTaLMHeadModel,
              TFGPTaMainLayer,
              TFGPTaModel,
              TFGPTaPreTrainedModel,
          )
  
      try:
          if not is_keras_nlp_available():
              raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
          pass
      else:
          from .tokenization_gpta_tf import TFGPTaTokenizer
  
      try:
          if not is_flax_available():
              raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
          pass
      else:
          from .modeling_flax_gpta import FlaxGPTaLMHeadModel, FlaxGPTaModel, FlaxGPTaPreTrainedModel
  
  else:
      import sys
  
      _A						=     _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)
  
  