



from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch



@dataclass
class     _UpperCAmelCase			:
     UpperCamelCase__		    =				42  # [batch_size x 3]
     UpperCamelCase__		    =				42  # [batch_size x 3]
     UpperCamelCase__		    =				42  # [batch_size x 3]
     UpperCamelCase__		    =				42  # [batch_size x 3]
     UpperCamelCase__		    =				42
     UpperCamelCase__		    =				42
     UpperCamelCase__		    =				42
     UpperCamelCase__		    =				42
     UpperCamelCase__		    =				42




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




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




     def 		snake_case_		(				self):
         A__		 =					torch.arange(self.height * self.width)
         A__		 =					torch.stack(
             [
                 pixel_indices % self.width,
                 torch.div(a__ ,						self.width ,						rounding_mode='''trunc'''),
             ] ,						axis=1 ,						)
         return coords




     @property
     def 		snake_case_		(				self):
         A__ ,	*A__		 =					self.shape
         A__		 =					int(np.prod(a__))

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

         A__		 =					rays.view(a__ ,						inner_batch_size * self.height * self.width ,						2 ,						3)

         return rays




     def 		snake_case_		(				self ,						a__):
         A__ ,	*A__ ,	A__		 =					coords.shape
         assert n_coords == 2
         assert batch_size == self.origin.shape[0]

         A__		 =					coords.view(a__ ,						-1 ,						2)

         A__		 =					self.resolution()
         A__		 =					self.fov()

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

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




     def 		snake_case_		(				self ,						a__ ,						a__):
         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=a__ ,						height=a__ ,						x_fov=self.x_fov ,						y_fov=self.y_fov ,						)







def 		lowerCAmelCase__    (					UpperCamelCase_				:       int	)->  DifferentiableProjectiveCamera:
    A__		 =					[]
    A__		 =					[]
    A__		 =					[]
    A__		 =					[]
    for theta in np.linspace(0 ,       2 * np.pi ,       num=2_0	):
        A__		 =					np.array([np.sin(UpperCamelCase_	), np.cos(UpperCamelCase_	), -0.5]	)
        z /= np.sqrt(np.sum(z**2	)	)
        A__		 =					-z * 4
        A__		 =					np.array([np.cos(UpperCamelCase_	), -np.sin(UpperCamelCase_	), 0.0]	)
        A__		 =					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_	)) ,       )








from __future__ import annotations



def 		lowerCAmelCase__    (					UpperCamelCase_				:       str ,       UpperCamelCase_				:       list[str] | None = None	)->  list[list[str]]:
    A__		 =					word_bank or []
    # create a table
    A__		 =					len(UpperCamelCase_	) + 1

    A__		 =					[]
    for _ in range(UpperCamelCase_	):
        table.append([]	)
    # seed value
    A__		 =					[[]]  # 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:
                    A__		 =					[
                        [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"],
       )
   )
