
def       A       (					lowercase )   ->  int:
		'''simple docstring'''

		assert isinstance(lowercase    ,       lowercase ), f'''The input value of [n={number}] is not an integer'''

		if number == 1:
				return 2
		elif number < 1:
				UpperCamelCase		=     f'''The input value of [n={number}] has to be > 0'''
				raise ValueError(lowercase )
		else:
				UpperCamelCase		=     sylvester(number - 1 )
				UpperCamelCase		=     num - 1
				UpperCamelCase		=     num
				return lower * upper + 1


if __name__ == "__main__":
					print(F'''The 8th number in Sylvester\'s sequence: {sylvester(8)}''')


import numpy as np
import torch
import tqdm

from ...models.unet_ad import UNetaDModel
from ...pipelines import DiffusionPipeline
from ...utils import randn_tensor
from ...utils.dummy_pt_objects import DDPMScheduler


class 				lowercase					(		_SCREAMING_SNAKE_CASE   ):



		def __init__( self				,      A_				,      A_				,      A_				,      A_				,      )  ->					Optional[int]:
				"""simple docstring"""
				super().__init__()
				UpperCamelCase		=     value_function
				UpperCamelCase		=     unet
				UpperCamelCase		=     scheduler
				UpperCamelCase		=     env
				UpperCamelCase		=     env.get_dataset()
				UpperCamelCase		=     {}
				for key in self.data.keys():
						try:
								UpperCamelCase		=     self.data[key].mean()
						except:  # noqa: E722
								pass
				UpperCamelCase		=     {}
				for key in self.data.keys():
						try:
								UpperCamelCase		=     self.data[key].std()
						except:  # noqa: E722
								pass
				UpperCamelCase		=     env.observation_space.shape[0]
				UpperCamelCase		=     env.action_space.shape[0]



		def __UpperCamelCase ( self				,      A_				,      A_       )  ->					Optional[Any]:
				"""simple docstring"""
				return (x_in - self.means[key]) / self.stds[key]



		def __UpperCamelCase ( self				,      A_				,      A_       )  ->					Union[str, Any]:
				"""simple docstring"""
				return x_in * self.stds[key] + self.means[key]



		def __UpperCamelCase ( self				,      A_       )  ->					Any:
				"""simple docstring"""
				if type(A_       ) is dict:
						return {k: self.to_torch(A_       ) for k, v in x_in.items()}
				elif torch.is_tensor(A_       ):
						return x_in.to(self.unet.device       )
				return torch.tensor(A_				,      device=self.unet.device       )



		def __UpperCamelCase ( self				,      A_				,      A_				,      A_       )  ->					Optional[int]:
				"""simple docstring"""
				for key, val in cond.items():
						UpperCamelCase		=     val.clone()
				return x_in



		def __UpperCamelCase ( self				,      A_				,      A_				,      A_				,      A_       )  ->					Union[str, Any]:
				"""simple docstring"""
				UpperCamelCase		=     x.shape[0]
				UpperCamelCase		=     None
				for i in tqdm.tqdm(self.scheduler.timesteps       ):
						# create batch of timesteps to pass into model
						UpperCamelCase		=     torch.full((batch_size,)				,      A_				,      device=self.unet.device				,      dtype=torch.long       )
						for _ in range(A_       ):
								with torch.enable_grad():
										x.requires_grad_()

										# permute to match dimension for pre-trained models
										UpperCamelCase		=     self.value_function(x.permute(0				,      2				,      1       )				,      A_       ).sample
										UpperCamelCase		=     torch.autograd.grad([y.sum()]				,      [x]       )[0]

										UpperCamelCase		=     self.scheduler._get_variance(A_       )
										UpperCamelCase		=     torch.exp(0.5 * posterior_variance       )
										UpperCamelCase		=     model_std * grad

								UpperCamelCase		=     0
								UpperCamelCase		=     x.detach()
								UpperCamelCase		=     x + scale * grad
								UpperCamelCase		=     self.reset_xa(A_				,      A_				,      self.action_dim       )

						UpperCamelCase		=     self.unet(x.permute(0				,      2				,      1       )				,      A_       ).sample.permute(0				,      2				,      1       )

						# TODO: verify deprecation of this kwarg
						UpperCamelCase		=     self.scheduler.step(A_				,      A_				,      A_				,      predict_epsilon=A_       )['prev_sample']

						# apply conditions to the trajectory (set the initial state)
						UpperCamelCase		=     self.reset_xa(A_				,      A_				,      self.action_dim       )
						UpperCamelCase		=     self.to_torch(A_       )
				return x, y



		def __call__( self				,      A_				,      A_=64				,      A_=32				,      A_=2				,      A_=0.1       )  ->					List[str]:
				"""simple docstring"""
				# normalize the observations and create  batch dimension
				UpperCamelCase		=     self.normalize(A_				,      'observations'       )
				UpperCamelCase		=     obs[None].repeat(A_				,      axis=0       )

				UpperCamelCase		=     {0: self.to_torch(A_       )}
				UpperCamelCase		=     (batch_size, planning_horizon, self.state_dim + self.action_dim)

				# generate initial noise and apply our conditions (to make the trajectories start at current state)
				UpperCamelCase		=     randn_tensor(A_				,      device=self.unet.device       )
				UpperCamelCase		=     self.reset_xa(A_				,      A_				,      self.action_dim       )
				UpperCamelCase		=     self.to_torch(A_       )

				# run the diffusion process
				UpperCamelCase	,  UpperCamelCase		=     self.run_diffusion(A_				,      A_				,      A_				,      A_       )

				# sort output trajectories by value
				UpperCamelCase		=     y.argsort(0				,      descending=A_       ).squeeze()
				UpperCamelCase		=     x[sorted_idx]
				UpperCamelCase		=     sorted_values[:, :, : self.action_dim]
				UpperCamelCase		=     actions.detach().cpu().numpy()
				UpperCamelCase		=     self.de_normalize(A_				,      key='actions'       )

				# select the action with the highest value
				if y is not None:
						UpperCamelCase		=     0
				else:
						# if we didn't run value guiding, select a random action
						UpperCamelCase		=     np.random.randint(0				,      A_       )

				UpperCamelCase		=     denorm_actions[selected_index, 0]
				return denorm_actions
