"""simple docstring"""




from __future__ import annotations





def 		__lowerCamelCase							(UpperCAmelCase__       :							str ,	UpperCAmelCase__       :							list[str] | None = None					):
					SCREAMING_SNAKE_CASE           =    word_bank or []
					# create a table
					SCREAMING_SNAKE_CASE           =    len(UpperCAmelCase__					) + 1

					SCREAMING_SNAKE_CASE           =    []
					for _ in range(UpperCAmelCase__					):
										table.append([]					)
					# seed value
					SCREAMING_SNAKE_CASE           =    [[]]  # because empty string has empty combination

					# iterate through the indices
					for i in range(UpperCAmelCase__					):
										# condition
										if table[i] != []:
															for word in word_bank:
																				# slice condition
																				if target[i : i + len(UpperCAmelCase__					)] == word:
																									SCREAMING_SNAKE_CASE           =    [
																									    [word, *way] for way in table[i]
																									]
																									# adds the word to every combination the current position holds
																									# now,push that combination to the table[i+len(word)]
																									table[i + len(UpperCAmelCase__					)] += new_combinations

    # combinations are in reverse order so reverse for better output
					for combination in table[len(UpperCAmelCase__					)]:
										combination.reverse()

					return table[len(UpperCAmelCase__					)]


if __name__ == "__main__":
							print(all_construct('''jwajalapa''', ['''jwa''', '''j''', '''w''', '''a''', '''la''', '''lapa''']))
							print(all_construct('''rajamati''', ['''s''', '''raj''', '''amat''', '''raja''', '''ma''', '''i''', '''t''']))
							print(
							    all_construct(
							        '''hexagonosaurus''',
							        ['''h''', '''ex''', '''hex''', '''ag''', '''ago''', '''ru''', '''auru''', '''rus''', '''go''', '''no''', '''o''', '''s'''],
							    )
							)





from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch


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




							def 		__snake_case(  self				:   str )   ->			Dict:



												'''simple docstring'''

												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 		__snake_case(  self				:   int )   ->			str:



												'''simple docstring'''

												return torch.from_numpy(np.array([self.width, self.height]		,							dtype=np.floataa ) )




							def 		__snake_case(  self				:   Tuple )   ->			List[str]:



												'''simple docstring'''

												return torch.from_numpy(np.array([self.x_fov, self.y_fov]		,							dtype=np.floataa ) )




							def 		__snake_case(  self				:   Any )   ->			torch.Tensor:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE           =    torch.arange(self.height * self.width )
												SCREAMING_SNAKE_CASE           =    torch.stack(
												    [
												        pixel_indices % self.width,
												        torch.div(_UpperCamelCase		,							self.width		,							rounding_mode="trunc" ),
												    ]		,							axis=1		,							)
												return coords




							@property
							def 		__snake_case(  self				:   Any )   ->			Tuple:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE     ,				*SCREAMING_SNAKE_CASE           =    self.shape
												SCREAMING_SNAKE_CASE           =    int(np.prod(_UpperCamelCase ) )

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

												SCREAMING_SNAKE_CASE           =    rays.view(_UpperCamelCase		,							inner_batch_size * self.height * self.width		,							2		,							3 )

												return rays




							def 		__snake_case(  self				:   Optional[int]		,							_UpperCamelCase				:   torch.Tensor )   ->			torch.Tensor:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE     ,				*SCREAMING_SNAKE_CASE     ,				SCREAMING_SNAKE_CASE           =    coords.shape
												assert n_coords == 2
												assert batch_size == self.origin.shape[0]

												SCREAMING_SNAKE_CASE           =    coords.view(_UpperCamelCase		,							-1		,							2 )

												SCREAMING_SNAKE_CASE           =    self.resolution()
												SCREAMING_SNAKE_CASE           =    self.fov()

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

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





							def 		__snake_case(  self				:   List[Any]		,							_UpperCamelCase				:   int		,							_UpperCamelCase				:   int )   ->			"DifferentiableProjectiveCamera":



												'''simple docstring'''

												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=_UpperCamelCase		,							height=_UpperCamelCase		,							x_fov=self.x_fov		,							y_fov=self.y_fov		,							)





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




