



from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch





@dataclass
class    lowerCamelCase__  :
     """simple docstring"""



     _A       =			42  # [batch_size x 3]
     _A       =			42  # [batch_size x 3]
     _A       =			42  # [batch_size x 3]
     _A       =			42  # [batch_size x 3]
     _A       =			42
     _A       =			42
     _A       =			42
     _A       =			42
     _A       =			42







     def 						_a      (self    ):






           '''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 						_a      (self    ):






           '''simple docstring'''



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







     def 						_a      (self    ):






           '''simple docstring'''



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







     def 						_a      (self    ):






           '''simple docstring'''



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







     @property
     def 						_a      (self    ):






           '''simple docstring'''



           lowerCamelCase								=		self.shape
           lowerCamelCase								=		int(np.prod(UpperCamelCase__    )    )

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

           lowerCamelCase								=		rays.view(UpperCamelCase__				,			inner_batch_size * self.height * self.width				,			2				,			3    )

           return rays







     def 						_a      (self				,			__a    ):






           '''simple docstring'''



           lowerCamelCase								=		coords.shape
           assert n_coords == 2
           assert batch_size == self.origin.shape[0]

           lowerCamelCase								=		coords.view(UpperCamelCase__				,			-1				,			2    )

           lowerCamelCase								=		self.resolution()
           lowerCamelCase								=		self.fov()

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

           lowerCamelCase								=		fracs.view(UpperCamelCase__				,			-1				,			2    )
           lowerCamelCase								=		(
               self.z.view(UpperCamelCase__				,			1				,			3    )
               + self.x.view(UpperCamelCase__				,			1				,			3    ) * fracs[:, :, :1]
               + self.y.view(UpperCamelCase__				,			1				,			3    ) * fracs[:, :, 1:]
           )
           lowerCamelCase								=		directions / directions.norm(dim=-1				,			keepdim=UpperCamelCase__    )
           lowerCamelCase								=		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 						_a      (self				,			__a				,			__a    ):






           '''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     __lowercase(	UpperCAmelCase__ ):


      """simple docstring"""



      lowerCamelCase								=		[]
      lowerCamelCase								=		[]
      lowerCamelCase								=		[]
      lowerCamelCase								=		[]
      for theta in np.linspace(0   ,   2 * np.pi   ,   num=20 ):
            lowerCamelCase								=		np.array([np.sin(_lowercase ), np.cos(_lowercase ), -0.5] )
            z /= np.sqrt(np.sum(z**2 ) )
            lowerCamelCase								=		-z * 4
            lowerCamelCase								=		np.array([np.cos(_lowercase ), -np.sin(_lowercase ), 0.0] )
            lowerCamelCase								=		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 ))   ,   )








def     __lowercase(	UpperCAmelCase__ ):


      """simple docstring"""



      lowerCamelCase								=		[]
      lowerCamelCase								=		[]
      lowerCamelCase								=		{
          "^": 3,
          "*": 2,
          "/": 2,
          "%": 2,
          "+": 1,
          "-": 1,
      }  # Priority of each operator
      lowerCamelCase								=		len(UpperCAmelCase__ ) if (len(UpperCAmelCase__ ) > 7) else 7

      # Print table header for output
      print(
          "Symbol".center(8 )   ,   "Stack".center(UpperCAmelCase__ )   ,   "Postfix".center(UpperCAmelCase__ )   ,   sep=" | "   ,   )
      print("-" * (print_width * 3 + 7) )

      for x in infix:
            if x.isalpha() or x.isdigit():
                  post_fix.append(UpperCAmelCase__ )  # if x is Alphabet / Digit, add it to Postfix
            elif x == "(":
                  stack.append(UpperCAmelCase__ )  # if x is "(" push to Stack
            elif x == ")":  # if x is ")" pop stack until "(" is encountered
                  while stack[-1] != "(":
                        post_fix.append(stack.pop() )  # Pop stack & add the content to Postfix
                  stack.pop()
            else:
                  if len(UpperCAmelCase__ ) == 0:
                        stack.append(UpperCAmelCase__ )  # If stack is empty, push x to stack
                  else:  # while priority of x is not > priority of element in the stack
                        while len(UpperCAmelCase__ ) > 0 and priority[x] <= priority[stack[-1]]:
                              post_fix.append(stack.pop() )  # pop stack & add to Postfix
                        stack.append(UpperCAmelCase__ )  # push x to stack

            print(
                x.center(8 )   ,   ("".join(UpperCAmelCase__ )).ljust(UpperCAmelCase__ )   ,   ("".join(UpperCAmelCase__ )).ljust(UpperCAmelCase__ )   ,   sep=" | "   ,   )  # Output in tabular format

      while len(UpperCAmelCase__ ) > 0:  # while stack is not empty
            post_fix.append(stack.pop() )  # pop stack & add to Postfix
            print(
                " ".center(8 )   ,   ("".join(UpperCAmelCase__ )).ljust(UpperCAmelCase__ )   ,   ("".join(UpperCAmelCase__ )).ljust(UpperCAmelCase__ )   ,   sep=" | "   ,   )  # Output in tabular format

      return "".join(UpperCAmelCase__ )  # return Postfix as str

def     __lowercase(	UpperCAmelCase__ ):


      """simple docstring"""



      lowerCamelCase								=		list(infix[::-1] )  # reverse the infix equation

      for i in range(len(UpperCAmelCase__ ) ):
            if infix[i] == "(":
                  lowerCamelCase								=		")"  # change "(" to ")"
            elif infix[i] == ")":
                  lowerCamelCase								=		"("  # change ")" to "("

      return (infix_2_postfix("".join(UpperCAmelCase__ ) ))[
          ::-1
      ]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
     a_						:     str	     =		input('\nEnter an Infix Equation = ')  # Input an Infix equation
     a_						:     List[Any]	     =		''.join(Infix.split())  # Remove spaces from the input
     print('\n\t', Infix, '(Infix) -> ', infix_2_prefix(Infix), '(Prefix)')