


from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch







@dataclass
class lowerCAmelCase_		:

 '''simple docstring'''

 __snake_case				=						4_2  # [batch_size x 3]
 __snake_case				=						4_2  # [batch_size x 3]
 __snake_case				=						4_2  # [batch_size x 3]
 __snake_case				=						4_2  # [batch_size x 3]
 __snake_case				=						4_2
 __snake_case				=						4_2
 __snake_case				=						4_2
 __snake_case				=						4_2
 __snake_case				=						4_2



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



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



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



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

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

       snake_case_ =   rays.view(_UpperCAmelCase	,   inner_batch_size * self.height * self.width	,   2	,   3      )

       return rays



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

       snake_case_ =   coords.view(_UpperCAmelCase	,   -1	,   2      )

       snake_case_ =   self.resolution()
       snake_case_ =   self.fov()

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

       snake_case_ =   fracs.view(_UpperCAmelCase	,   -1	,   2      )
       snake_case_ =   (
           self.z.view(_UpperCAmelCase	,   1	,   3      )
           + self.x.view(_UpperCAmelCase	,   1	,   3      ) * fracs[:, :, :1]
           + self.y.view(_UpperCAmelCase	,   1	,   3      ) * fracs[:, :, 1:]
       )
       snake_case_ =   directions / directions.norm(dim=-1	,   keepdim=_UpperCAmelCase      )
       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 		UpperCamelCase__  (			self	,   _UpperCAmelCase	,   _UpperCAmelCase      ):
       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					(SCREAMING_SNAKE_CASE      )->						DifferentiableProjectiveCamera:




      """simple docstring"""

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



def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE = 6008_5147_5143      )->						int:




      """simple docstring"""

      try:
            snake_case_ =   int(SCREAMING_SNAKE_CASE      )
      except (TypeError, ValueError):
            raise TypeError('''Parameter n must be int or castable to int.'''      )
      if n <= 0:
            raise ValueError('''Parameter n must be greater than or equal to one.'''      )
      snake_case_ =   1
      snake_case_ =   2
      while i * i <= n:
            while n % i == 0:
                  snake_case_ =   i
                  n //= i
            i += 1
      if n > 1:
            snake_case_ =   n
      return int(SCREAMING_SNAKE_CASE      )


if __name__ == "__main__":
   print(f'''{solution() = }''')