
from itertools import combinations, product


def 		_lowerCamelCase       (   _a			,   _a			,   _a			,   _a  ):
  """simple docstring"""




  if xa == ya == 0 or xa == ya == 0:
    return False
  _lowerCamelCase      =						xa * xa + ya * ya
  _lowerCamelCase      =						xa * xa + ya * ya
  _lowerCamelCase      =						(xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
  return (
      a_square + b_square == c_square
      or a_square + c_square == b_square
      or b_square + c_square == a_square
  )


def 		_lowerCamelCase       (   _a = 5_0  ):
  """simple docstring"""




  return sum(
      1
      for pta, pta in combinations(product(range(limit + 1  )			,   repeat=2  )			,   2  )
      if is_right(*_a			,   *_a  )  )


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






import torch

from diffusers import LMSDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest


class 			UpperCamelCase_				(  A     ):




      '''simple docstring'''







      a		:Any						 =      (LMSDiscreteScheduler,)
      a		:Dict						 =      10







      def lowercase__		( self					,					**_UpperCAmelCase):
            lowerCAmelCase_						=      {
                '''num_train_timesteps''': 1_100,
                '''beta_start''': 0.0001,
                '''beta_end''': 0.02,
                '''beta_schedule''': '''linear''',
            }

            config.update(**_UpperCAmelCase)
            return config







      def lowercase__		( self):
            for timesteps in [10, 50, 100, 1_000]:
                  self.check_over_configs(num_train_timesteps=_UpperCAmelCase)







      def lowercase__		( self):
            for beta_start, beta_end in zip([0.00001, 0.0001, 0.001]					,					[0.0002, 0.002, 0.02]):
                  self.check_over_configs(beta_start=_UpperCAmelCase					,					beta_end=_UpperCAmelCase)







      def lowercase__		( self):
            for schedule in ["linear", "scaled_linear"]:
                  self.check_over_configs(beta_schedule=_UpperCAmelCase)







      def lowercase__		( self):
            for prediction_type in ["epsilon", "v_prediction"]:
                  self.check_over_configs(prediction_type=_UpperCAmelCase)







      def lowercase__		( self):
            for t in [0, 500, 800]:
                  self.check_over_forward(time_step=_UpperCAmelCase)







      def lowercase__		( self):
            lowerCAmelCase_						=      self.scheduler_classes[0]
            lowerCAmelCase_						=      self.get_scheduler_config()
            lowerCAmelCase_						=      scheduler_class(**_UpperCAmelCase)

            scheduler.set_timesteps(self.num_inference_steps)

            lowerCAmelCase_						=      self.dummy_model()
            lowerCAmelCase_						=      self.dummy_sample_deter * scheduler.init_noise_sigma

            for i, t in enumerate(scheduler.timesteps):
                  lowerCAmelCase_						=      scheduler.scale_model_input(_UpperCAmelCase					,					_UpperCAmelCase)

                  lowerCAmelCase_						=      model(_UpperCAmelCase					,					_UpperCAmelCase)

                  lowerCAmelCase_						=      scheduler.step(_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase)
                  lowerCAmelCase_						=      output.prev_sample

            lowerCAmelCase_						=      torch.sum(torch.abs(_UpperCAmelCase))
            lowerCAmelCase_						=      torch.mean(torch.abs(_UpperCAmelCase))

            assert abs(result_sum.item() - 1006.388) < 1E-2
            assert abs(result_mean.item() - 1.31) < 1E-3







      def lowercase__		( self):
            lowerCAmelCase_						=      self.scheduler_classes[0]
            lowerCAmelCase_						=      self.get_scheduler_config(prediction_type='''v_prediction''')
            lowerCAmelCase_						=      scheduler_class(**_UpperCAmelCase)

            scheduler.set_timesteps(self.num_inference_steps)

            lowerCAmelCase_						=      self.dummy_model()
            lowerCAmelCase_						=      self.dummy_sample_deter * scheduler.init_noise_sigma

            for i, t in enumerate(scheduler.timesteps):
                  lowerCAmelCase_						=      scheduler.scale_model_input(_UpperCAmelCase					,					_UpperCAmelCase)

                  lowerCAmelCase_						=      model(_UpperCAmelCase					,					_UpperCAmelCase)

                  lowerCAmelCase_						=      scheduler.step(_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase)
                  lowerCAmelCase_						=      output.prev_sample

            lowerCAmelCase_						=      torch.sum(torch.abs(_UpperCAmelCase))
            lowerCAmelCase_						=      torch.mean(torch.abs(_UpperCAmelCase))

            assert abs(result_sum.item() - 0.0017) < 1E-2
            assert abs(result_mean.item() - 2.2676E-06) < 1E-3







      def lowercase__		( self):
            lowerCAmelCase_						=      self.scheduler_classes[0]
            lowerCAmelCase_						=      self.get_scheduler_config()
            lowerCAmelCase_						=      scheduler_class(**_UpperCAmelCase)

            scheduler.set_timesteps(self.num_inference_steps					,					device=_UpperCAmelCase)

            lowerCAmelCase_						=      self.dummy_model()
            lowerCAmelCase_						=      self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
            lowerCAmelCase_						=      sample.to(_UpperCAmelCase)

            for i, t in enumerate(scheduler.timesteps):
                  lowerCAmelCase_						=      scheduler.scale_model_input(_UpperCAmelCase					,					_UpperCAmelCase)

                  lowerCAmelCase_						=      model(_UpperCAmelCase					,					_UpperCAmelCase)

                  lowerCAmelCase_						=      scheduler.step(_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase)
                  lowerCAmelCase_						=      output.prev_sample

            lowerCAmelCase_						=      torch.sum(torch.abs(_UpperCAmelCase))
            lowerCAmelCase_						=      torch.mean(torch.abs(_UpperCAmelCase))

            assert abs(result_sum.item() - 1006.388) < 1E-2
            assert abs(result_mean.item() - 1.31) < 1E-3







      def lowercase__		( self):
            lowerCAmelCase_						=      self.scheduler_classes[0]
            lowerCAmelCase_						=      self.get_scheduler_config()
            lowerCAmelCase_						=      scheduler_class(**_UpperCAmelCase					,					use_karras_sigmas=_UpperCAmelCase)

            scheduler.set_timesteps(self.num_inference_steps					,					device=_UpperCAmelCase)

            lowerCAmelCase_						=      self.dummy_model()
            lowerCAmelCase_						=      self.dummy_sample_deter.to(_UpperCAmelCase) * scheduler.init_noise_sigma
            lowerCAmelCase_						=      sample.to(_UpperCAmelCase)

            for t in scheduler.timesteps:
                  lowerCAmelCase_						=      scheduler.scale_model_input(_UpperCAmelCase					,					_UpperCAmelCase)

                  lowerCAmelCase_						=      model(_UpperCAmelCase					,					_UpperCAmelCase)

                  lowerCAmelCase_						=      scheduler.step(_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase)
                  lowerCAmelCase_						=      output.prev_sample

            lowerCAmelCase_						=      torch.sum(torch.abs(_UpperCAmelCase))
            lowerCAmelCase_						=      torch.mean(torch.abs(_UpperCAmelCase))

            assert abs(result_sum.item() - 3812.9927) < 2E-2
            assert abs(result_mean.item() - 4.9648) < 1E-3



