
from __future__ import annotations

from collections.abc import Iterable, Iterator
from dataclasses import dataclass

__A							=(3, 9, -1_1, 0, 7, 5, 1, -1)
__A							=(4, 6, 2, 0, 8, 1_0, 3, -2)




@dataclass
class        _SCREAMING_SNAKE_CASE	:
	lowerCAmelCase__   =					42
	lowerCAmelCase__   =					42




class        _SCREAMING_SNAKE_CASE	:



	def __init__(       self		,    lowercase					)							->			None:
					lowerCamelCase_         =     None
					for i in sorted(lowercase		,    reverse=lowercase					):
									lowerCamelCase_         =     Node(lowercase		,    self.head					)



	def __iter__(       self					)							->			Iterator[int]:
					lowerCamelCase_         =     self.head
					while node:
									yield node.data
									lowerCamelCase_         =     node.next_node



	def __len__(       self					)							->			int:
					return sum(1 for _ in self					)



	def __str__(       self					)							->			str:
					return " -> ".join([str(lowercase					) for node in self]					)





def      lowerCamelCase_					(							lowerCamelCase__      ,					lowerCamelCase__       ):
				return SortedLinkedList(list(lowerCamelCase__       ) + list(lowerCamelCase__       )       )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			__A							=SortedLinkedList
			print(merge_lists(SSL(test_data_odd), SSL(test_data_even)))




from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch




@dataclass
class        _SCREAMING_SNAKE_CASE	:
	lowerCAmelCase__   =					42  # [batch_size x 3]
	lowerCAmelCase__   =					42  # [batch_size x 3]
	lowerCAmelCase__   =					42  # [batch_size x 3]
	lowerCAmelCase__   =					42  # [batch_size x 3]
	lowerCAmelCase__   =					42
	lowerCAmelCase__   =					42
	lowerCAmelCase__   =					42
	lowerCAmelCase__   =					42
	lowerCAmelCase__   =					42



	def        SCREAMING_SNAKE_CASE_(       self					)							->			Optional[int]:
					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        SCREAMING_SNAKE_CASE_(       self					)							->			str:
					return torch.from_numpy(np.array([self.width, self.height]		,    dtype=np.floataa					)					)



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



	def        SCREAMING_SNAKE_CASE_(       self					)							->			torch.Tensor:
					lowerCamelCase_         =     torch.arange(self.height * self.width					)
					lowerCamelCase_         =     torch.stack(
					    [
					        pixel_indices % self.width,
					        torch.div(lowercase		,    self.width		,    rounding_mode="trunc"					),
					    ]		,    axis=1		,    )
					return coords



	@property
	def        SCREAMING_SNAKE_CASE_(       self					)							->			Dict:
					lowerCamelCase_      ,       *lowerCamelCase_         =     self.shape
					lowerCamelCase_         =     int(np.prod(lowercase					)					)

					lowerCamelCase_         =     self.get_image_coords()
					lowerCamelCase_         =     torch.broadcast_to(coords.unsqueeze(0					)		,    [batch_size * inner_batch_size, *coords.shape]					)
					lowerCamelCase_         =     self.get_camera_rays(lowercase					)

					lowerCamelCase_         =     rays.view(lowercase		,    inner_batch_size * self.height * self.width		,    2		,    3					)

					return rays



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase					)							->			torch.Tensor:
					lowerCamelCase_      ,       *lowerCamelCase_      ,       lowerCamelCase_         =     coords.shape
					assert n_coords == 2
					assert batch_size == self.origin.shape[0]

					lowerCamelCase_         =     coords.view(lowercase		,    -1		,    2					)

					lowerCamelCase_         =     self.resolution()
					lowerCamelCase_         =     self.fov()

					lowerCamelCase_         =     (flat.float() / (res - 1)) * 2 - 1
					lowerCamelCase_         =     fracs * torch.tan(fov / 2					)

					lowerCamelCase_         =     fracs.view(lowercase		,    -1		,    2					)
					lowerCamelCase_         =     (
					    self.z.view(lowercase		,    1		,    3					)
					    + self.x.view(lowercase		,    1		,    3					) * fracs[:, :, :1]
					    + self.y.view(lowercase		,    1		,    3					) * fracs[:, :, 1:]
					)
					lowerCamelCase_         =     directions / directions.norm(dim=-1		,    keepdim=lowercase					)
					lowerCamelCase_         =     torch.stack(
					    [
					        torch.broadcast_to(self.origin.view(lowercase		,    1		,    3					)		,    [batch_size, directions.shape[1], 3]					),
					        directions,
					    ]		,    dim=2		,    )
					return rays.view(lowercase		,    *lowercase		,    2		,    3					)



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase		,    lowercase					)							->			"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=lowercase		,    height=lowercase		,    x_fov=self.x_fov		,    y_fov=self.y_fov		,    )





def      lowerCamelCase_					(							lowerCamelCase__       ):
				lowerCamelCase_         =     []
				lowerCamelCase_         =     []
				lowerCamelCase_         =     []
				lowerCamelCase_         =     []
				for theta in np.linspace(0      ,					2 * np.pi      ,					num=2_0       ):
								lowerCamelCase_         =     np.array([np.sin(lowerCamelCase__       ), np.cos(lowerCamelCase__       ), -0.5]       )
								z /= np.sqrt(np.sum(z**2       )       )
								lowerCamelCase_         =     -z * 4
								lowerCamelCase_         =     np.array([np.cos(lowerCamelCase__       ), -np.sin(lowerCamelCase__       ), 0.0]       )
								lowerCamelCase_         =     np.cross(lowerCamelCase__      ,					lowerCamelCase__       )
								origins.append(lowerCamelCase__       )
								xs.append(lowerCamelCase__       )
								ys.append(lowerCamelCase__       )
								zs.append(lowerCamelCase__       )
				return DifferentiableProjectiveCamera(
				    origin=torch.from_numpy(np.stack(lowerCamelCase__      ,					axis=0       )       ).float()      ,					x=torch.from_numpy(np.stack(lowerCamelCase__      ,					axis=0       )       ).float()      ,					y=torch.from_numpy(np.stack(lowerCamelCase__      ,					axis=0       )       ).float()      ,					z=torch.from_numpy(np.stack(lowerCamelCase__      ,					axis=0       )       ).float()      ,					width=lowerCamelCase__      ,					height=lowerCamelCase__      ,					x_fov=0.7      ,					y_fov=0.7      ,					shape=(1, len(lowerCamelCase__       ))      ,					)


