

"""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() = }''')




"""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__)

