





"""simple docstring"""




from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch


@dataclass
class  __UpperCamelCase       :
							lowerCamelCase     :      torch.Tensor  # [batch_size x 3]
							lowerCamelCase     :      torch.Tensor  # [batch_size x 3]
							lowerCamelCase     :      torch.Tensor  # [batch_size x 3]
							lowerCamelCase     :      torch.Tensor  # [batch_size x 3]
							lowerCamelCase     :      int
							lowerCamelCase     :      int
							lowerCamelCase     :      float
							lowerCamelCase     :      float
							lowerCamelCase     :      Tuple[int]






							def 					__a     (     self   )			->				Union[str, Any]:
								assert self.x.shape[0] == self.y.shape[0] == self.z.shape[0] == self.origin.shape[0]
								assert self.x.shape[1] == self.y.shape[1] == self.z.shape[1] == self.origin.shape[1] == 3
								assert len(self.x.shape   ) == len(self.y.shape   ) == len(self.z.shape   ) == len(self.origin.shape   ) == 2






							def 					__a     (     self   )			->				Any:
								return torch.from_numpy(np.array([self.width, self.height]   ,      dtype=np.floataa   )   )






							def 					__a     (     self   )			->				str:
								return torch.from_numpy(np.array([self.x_fov, self.y_fov]   ,      dtype=np.floataa   )   )






							def 					__a     (     self   )			->				torch.Tensor:
								a   :	int			=       torch.arange(self.height * self.width   )
								a   :	Optional[int]			=       torch.stack(
								    [
								        pixel_indices % self.width,
								        torch.div(lowerCAmelCase__   ,      self.width   ,      rounding_mode="trunc"   ),
								    ]   ,      axis=1   ,      )
								return coords






							@property
							def 					__a     (     self   )			->				Optional[Any]:
								a, *a   :	Dict			=       self.shape
								a   :	Any			=       int(np.prod(lowerCAmelCase__   )   )

								a   :	Optional[int]			=       self.get_image_coords()
								a   :	List[str]			=       torch.broadcast_to(coords.unsqueeze(0   )   ,      [batch_size * inner_batch_size, *coords.shape]   )
								a   :	Dict			=       self.get_camera_rays(lowerCAmelCase__   )

								a   :	Tuple			=       rays.view(lowerCAmelCase__   ,      inner_batch_size * self.height * self.width   ,      2   ,      3   )

								return rays






							def 					__a     (     self   ,      lowerCAmelCase__   )			->				torch.Tensor:
								a, *a, a   :	List[Any]			=       coords.shape
								assert n_coords == 2
								assert batch_size == self.origin.shape[0]

								a   :	Optional[int]			=       coords.view(lowerCAmelCase__   ,      -1   ,      2   )

								a   :	Dict			=       self.resolution()
								a   :	Optional[Any]			=       self.fov()

								a   :	Optional[int]			=       (flat.float() / (res - 1)) * 2 - 1
								a   :	str			=       fracs * torch.tan(fov / 2   )

								a   :	Tuple			=       fracs.view(lowerCAmelCase__   ,      -1   ,      2   )
								a   :	List[Any]			=       (
								    self.z.view(lowerCAmelCase__   ,      1   ,      3   )
								    + self.x.view(lowerCAmelCase__   ,      1   ,      3   ) * fracs[:, :, :1]
								    + self.y.view(lowerCAmelCase__   ,      1   ,      3   ) * fracs[:, :, 1:]
								)
								a   :	Dict			=       directions / directions.norm(dim=-1   ,      keepdim=lowerCAmelCase__   )
								a   :	Union[str, Any]			=       torch.stack(
								    [
								        torch.broadcast_to(self.origin.view(lowerCAmelCase__   ,      1   ,      3   )   ,      [batch_size, directions.shape[1], 3]   ),
								        directions,
								    ]   ,      dim=2   ,      )
								return rays.view(lowerCAmelCase__   ,      *lowerCAmelCase__   ,      2   ,      3   )






							def 					__a     (     self   ,      lowerCAmelCase__   ,      lowerCAmelCase__   )			->				"DifferentiableProjectiveCamera":
								assert width * self.height == height * self.width, "The aspect ratio should not change."
								return DifferentiableProjectiveCamera(
								    origin=self.origin   ,      x=self.x   ,      y=self.y   ,      z=self.z   ,      width=lowerCAmelCase__   ,      height=lowerCAmelCase__   ,      x_fov=self.x_fov   ,      y_fov=self.y_fov   ,      )






def    _SCREAMING_SNAKE_CASE	(			_lowercase		:					int      )				->DifferentiableProjectiveCamera:






	'''simple docstring'''






	a   :	int			=       []
	a   :	str			=       []
	a   :	List[str]			=       []
	a   :	Optional[Any]			=       []
	for theta in np.linspace(0					, 2 * np.pi					, num=20      ):
		a   :	Optional[Any]			=       np.array([np.sin(_lowercase      ), np.cos(_lowercase      ), -0.5]      )
		z /= np.sqrt(np.sum(z**2      )      )
		a   :	Union[str, Any]			=       -z * 4
		a   :	Tuple			=       np.array([np.cos(_lowercase      ), -np.sin(_lowercase      ), 0.0]      )
		a   :	List[Any]			=       np.cross(_lowercase					, _lowercase      )
		origins.append(_lowercase      )
		xs.append(_lowercase      )
		ys.append(_lowercase      )
		zs.append(_lowercase      )
	return DifferentiableProjectiveCamera(
	    origin=torch.from_numpy(np.stack(_lowercase					, axis=0      )      ).float()					, x=torch.from_numpy(np.stack(_lowercase					, axis=0      )      ).float()					, y=torch.from_numpy(np.stack(_lowercase					, axis=0      )      ).float()					, z=torch.from_numpy(np.stack(_lowercase					, axis=0      )      ).float()					, width=_lowercase					, height=_lowercase					, x_fov=0.7					, y_fov=0.7					, shape=(1, len(_lowercase      ))					, )









"""simple docstring"""




def    _SCREAMING_SNAKE_CASE	(			_lowercase		:					int = 200      )				->int:






	'''simple docstring'''






	a   :	Dict			=       [1, 2, 5, 10, 20, 50, 100, 200]
	a   :	Optional[Any]			=       [0] * (pence + 1)
	a   :	List[Any]			=       1  # base case: 1 way to make 0 pence

	for coin in coins:
		for i in range(_lowercase					, pence + 1					, 1      ):
			number_of_ways[i] += number_of_ways[i - coin]
	return number_of_ways[pence]


if __name__ == "__main__":
		assert solution(200) == 73682


