





from ...utils import is_note_seq_available, is_transformers_available, is_torch_available
from ...utils import OptionalDependencyNotAvailable


try:
     if not (is_transformers_available() and is_torch_available()):
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
     from .notes_encoder import SpectrogramNotesEncoder
     from .continous_encoder import SpectrogramContEncoder
     from .pipeline_spectrogram_diffusion import (
         SpectrogramContEncoder,
         SpectrogramDiffusionPipeline,
         TaFilmDecoder,
     )

try:
     if not (is_transformers_available() and is_torch_available() and is_note_seq_available()):
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ...utils.dummy_transformers_and_torch_and_note_seq_objects import *  # noqa F403
else:
     from .midi_utils import MidiProcessor





'''simple docstring'''



from collections import defaultdict
from math import gcd



def      UpperCAmelCase__   (      UpperCAmelCase_       :							int = 1_50_00_00				)	->						int:
     __lowerCamelCase  :      defaultdict														=						defaultdict(UpperCAmelCase_				)
     __lowerCamelCase  :      Any														=						2
     while 2 * euclid_m * (euclid_m + 1) <= limit:
          for euclid_n in range((euclid_m % 2) + 1 ,       UpperCAmelCase_ ,       2				):
               if gcd(UpperCAmelCase_ ,       UpperCAmelCase_				) > 1:
                    continue
               __lowerCamelCase  :      Any														=						2 * euclid_m * (euclid_m + euclid_n)
               for perimeter in range(UpperCAmelCase_ ,       limit + 1 ,       UpperCAmelCase_				):
                    frequencies[perimeter] += 1
          euclid_m += 1
     return sum(1 for frequency in frequencies.values() if frequency == 1				)


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






